Sea anemones are cnidarians belonging to the order Actiniaria, which is further divided into suborders, infraorders, families, genera and species. The approximately 1,000 sea anemone species identified are classified into four suborders: Endocoelantheae, Nyantheae, Protantheae and Ptychodacteae. Anemones are divided based on differences in physiology.
Sea anemones are grouped into the suborder Endocoelantheae because they have well-developed pedal discs but have no basilar muscles, which are muscles that connect the disc to the body walls. Their body columns are smooth. Suborder Endocoelantheae is divided into two families, Actinernidae and Halcuriidae. Anemones in the family Halcuriidae have elongated bodies with no lobes. They have fewer tentacles than most anemones, having only up to 70. This family is split into the genera Halcurias and Carlgrenia. Actinernidae anemones have thick bodies divided into four to eight lobes. Actinernidae includes the genera Synhalcurias, Isactinernus, Synactinernus and Actinernus.
Nyantheae contains the most anemone infraorders and families of any suborder by far. It contains the infraorders Athenaria, Boloceroidaria and Thenaria. Boloceroidaria contains two families, Boloceroididae and Nevadneidae. Athenaria contains 11 families and Thenaria is divided into 19 families. More anemones belong to the suborder Nyantheae than any other. Examples from the suborder Nyantheae include the burrowing anemone (Halcampa duodecimcirrata), the frilled anemone (Metridium senile), the swimming anemone (Stomphia coccinea) and the brightly-colored blister anemone (Phymactis papillosa).
Many species in the suborder Protantheae are commonly found in cold northern Atlantic waters. All anemones classified in the suborder Protantheae belong to the family Gonactiniidae. These anemones aren't capable of involution, or pulling their tentacles into their body tubes for protection. Their tentacles also can't retract. Protantheae is one of the anemone types that can reproduce asexually. Protanthea simplex is an example of a species classified in this suborder. Called sealoch anemones, they are very small, usually less than two inches tall, and populate coastal waters around Great Britain at depths of about 1,500 feet. Gonactinia prolifera is another species in this family. Both animals feed on particles floating in the ocean water.
The suborder Ptychodacteae includes the Antarctic anemones. These animals grow slowly but can reach rather large sizes for anemones, for instance Urticina antarctica grows to about six inches tall and wide. Ptychodacteae is subdivided into the families Preactiidae and Ptychodactiidae. Preactiidae is divided into two genera that contain one species each. Ptychodactiidae contains only one genus, Ptychodactis, which contains two species -- Ptychodactis patula and the recently-discovered Ptychodactis aleutiensis.


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Every Little Helps For EV Drivers
Wed 3rd Nov 2021
Motorists with electric cars can expect to take more than their shopping home with them when they visit one of the major supermarkets, with an influx of charging points ensuring that car can leave with a full charge.
Analysis from Zap-Map and the RAC has found that almost 2,000 charge points have been added to mainstream supermarkets over the last two years, with Tesco leading the way, with 922 chargers now available to shoppers free of charge thanks to a partnership with Volkswagen and Pod Point.
The boost in chargers means that supermarkets now accounts for eight per cent of the UK's 26,000 public chargers and there are 1,300 supermarkets with at least one EV charging device.
While Volkswagen and Pop Point haven't quite achieved their target of installing 2,400 charging points into Tesco stores, the grocery giant added 641 devices in the last two years, giving it a total of 922. Morrisons are also to be commended as they have the most number of rapid charge points, which should ensure a shopper can get a full charge during the average 45 minute shop.
Melanie Shufflebotham of Zap-Map said: "These facilities will be good both for 'top-up' charging and as a replacement for home charging.
"As we move towards 2030, it will be important for supermarkets not only to accelerate this roll-out but also to ensure that the consumer experience is as good as possible by providing 'open access' and simple payment options."
RAC director of EVs Sarah Winward-Kotecha said: "While the majority of drivers going electric will be fortunate enough to be able to charge easily on their driveways at home, for the remainder it won't be so easy so having access to free, or affordable, charging facilities at supermarkets is very important, and could even help accelerate EV take-up in the first place.
"Rapid charge points, in particular, make it possible to run an EV easily without access to a home charger as drivers can get their cars topped up in the time it takes them to do their weekly shop. We call on all the supermarket chains to let their customers know what to expect when it comes to EV charging provision and recognise the vital role they play in encouraging many more drivers to opt for electric cars next time they change their vehicles."

redpajama_set_name: RedPajamaCommonCrawl


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The Best Book Club eBooks
by A.D. Miller
A. D. Miller's Snowdrops is a riveting psychological drama that unfolds over the course of one Moscow winter, as a thirty-something Englishman's moral compass is spun by the seductive opportunities revealed to him by a new Russia: a land of hedonism and desperation, corruption and kindness, magical dachas and debauched nightclubs; a place where secrets — and corpses- come to light only when the deep snows start to thaw…
A chilling story of love and moral freefall: of the corruption, by a corrupt society, of a corruptible man. It is taut, intense and has a momentum as irresistible to the reder as the moral danger that first enchants, then threatens to overwhelm, its narrator.
Binocular Vision: New and Selected Stories
by Edith Pearlman
In this sumptuous offering, one of our premier storytellers provides a feast for fiction aficionados. Spanning four decades and three prize-winning collections, these 21 vintage selected stories and 13 scintillating new ones take us around the world, from Jerusalem to Central America, from tsarist Russia to London during the Blitz, from central Europe to Manhattan, and from the Maine coast to Godolphin, Massachusetts, a fictional suburb of Boston. These charged locales, and the lives of the endlessly varied characters within them, are evoked with a tenderness and incisiveness found in only our most observant seers.
The Good Daughter: A Memoir of My Mother's Hidden Life
by Jasmin Darznik
We were a world of two, my mother and I, until I started turning into an American girl. That's when she began telling me about The Good Daughter. It became a taunt, a warning, an omen.
Jasmin Darznik came to America from Iran when she was only three years old, and she grew up knowing very little about her family's history. When she was in her early twenties, on a day shortly following her father's death, Jasmin was helping her mother move; a photograph fell from a stack of old letters. The girl pictured was her mother. She was wearing a wedding veil, and at her side stood a man whom Jasmin had never seen before.
At first, Jasmin's mother, Lili, refused to speak about the photograph, and Jasmin returned to her own home frustrated and confused. But a few months later, she received from her mother the first of ten cassette tapes that would bring to light the wrenching hidden story of her family's true origins in Iran: Lili's marriage at thirteen, her troubled history of abuse and neglect, and a daughter she was forced to abandon in order to escape that life. The final tape revealed that Jasmin's sister, Sara — The Good Daughter — was still living in Iran.
In this sweeping, poignant, and beautifully written memoir, Jasmin weaves the stories of three generations of Iranian women into a unique tale of one family's struggle for freedom and understanding. The result is an enchanting and unforgettable story of secrets, betrayal, and the unbreakable mother-daughter bond.
Deep Down True
by Juliette Fay
From the author of Shelter Me-a funny and poignant novel about having your heart in the right place.
Newly divorced Dana Stellgarten has always been unfailingly nice- even to telemarketers-but now her temper is wearing thin. Money is tight, her kids are reeling from their dad's departure, and her Goth teenage niece has just landed on her doorstep. As she enters the slipstream of post-divorce romance and is befriended by the town queen bee, Dana finds that the tension between being true to yourself and being liked doesn't end in middle school… and that sometimes it takes a real friend to help you embrace adulthood in all its flawed complexity.
Bride of New France
by Suzanne Desrochers
In 1669, Laure Beausejour, an orphan imprisoned with prostitutes, the insane and other forgotten women in Paris' infamous Salpetriere, is sent across the Atlantic to New France as a Fille du roi. Laure once dreamed with her best friend Madeleine of using her needlework stills to become a seamstress on the Rue Saint-Honoré and to one day marry a gentleman. The King, however, needs French women in his new colony and he finds a fresh supply in the city's largest orphanage. Laure and Madeleine know little of the place called New France, except for stories of ferocious winters and men who eat the hearts of French priests. To be banished to Canada is a punishment worse than death.
Bride of New France explores the challenges of coming into womanhood in a brutal time and place. From the moment she arrives in Ville-Marie (Montreal), Laure is expected to marry and produce children with a French soldier who can himself barely survive the harsh conditions of his forest cabin. But Laure finds, through her clandestine relationship with Deskaheh, an allied Iroquois, a sense of the possibilities in this New World.
What happens to a woman who attempts to make her own life choices in such authoritative times?
Bride of New France is a beautiful debut novel that explores a fascinating chapter in Canadian history.
The Imperfectionists
by Tom Rachman
The Proper Care and Maintenance of Friendship
by Lisa Verge Higgins
What makes a wife a lover?
For Kate, the spark went out of her marriage long ago but her husband doesn't seem to notice. Their role as parents consumes their lives so they need to rekindle the romance they once shared.
What makes a woman a mother?
For Jo, a high-powered career has led her to believe that she doesn't have a single maternal instinct. When an orphan unexpectedly enters her life, she is forced to confront her own unhappy childhood and the walls it has built around her heart.
What makes a man the love of your life?
For Sarah, home is the steamy jungles of Africa while the man of her dreams waits in the air-conditioned confines of Los Angeles. Her longing for this man from the past is blinding her to a new love standing right in front of her.
What these women all have in common is a friend with a generous soul, an irrepressible spirit- and a serious illness. In her final letters, Rachel raises one last question: What makes a friend live in our hearts forever?
A Cup of Friendship
by Deborah Rodriguez
From the author of the memoir Kabul Beauty School comes a fiction debut as compelling as real life: the story of a remarkable coffee shop in the heart of Afghanistan, and the men and women who meet there — thrown together by circumstance, bonded by secrets, and united in an extraordinary friendship.
After hard luck and some bad choices, Sunny has finally found a place to call home — it just happens to be in the middle of a war zone.
The thirty-eight-year-old American's pride and joy is the Kabul Coffee House, where she brings hospitality to the expatriates, misfits, missionaries, and mercenaries who stroll through its doors. She's especially grateful that the busy days allow her to forget Tommy, the love of her life, who left her in pursuit of money and adventure.
Working alongside Sunny is the maternal Halajan, who vividly recalls the days before the Taliban and now must hide a modern romance from her ultratraditional son — who, unbeknownst to her, is facing his own religious doubts. Into the café come Isabel, a British journalist on the trail of a risky story; Jack, who left his family back home in Michigan to earn "danger pay" as a consultant; and Candace, a wealthy and well-connected American whose desire to help threatens to cloud her judgment.
When Yazmina, a young Afghan from a remote village, is kidnapped and left on a city street pregnant and alone, Sunny welcomes her into the café and gives her a home — but Yazmina hides a secret that could put all their lives in jeopardy.
As this group of men and women discover that there's more to one another than meets the eye, they'll form an unlikely friendship that will change not only their own lives but the lives of an entire country.
Brimming with Deborah Rodriguez's remarkable gift for depicting the nuances of life in Kabul, and filled with vibrant characters that readers will truly care about, A Cup of Friendship is the best kind of fiction — full of heart yet smart and thought-provoking.
Fall On Your Knees
by Ann-Marie MacDonald
They are the Pipers of Cape Breton Island — a family steeped in lies and unspoken truths that reach out from the past, forever mindful of the tragic secret that could shatter the family to its foundations.
Chronicling five generations of this eccentric clan, Fall On Your Knees follows four remarkable sisters whose lives are filled with driving ambition, inescapable family bonds, and forbidden love. Their experiences will take them from their stormswept homeland, across the battlefields of World War I, to the freedom and independence of Jazz-era New York City.
Compellingly written, running the literary gamut from menacingly dark to hilariously funny, this is an epic saga of one family's trials and triumphs in a world of sin, guilt, and redemption.
The Hangman's Daughter
by Oliver Pötzsch, Lee Chadeayne
Germany, 1660: When a dying boy is pulled from the river with a mark crudely tattooed on his shoulder, hangman Jakob Kuisl is called upon to investigate whether witchcraft is at play. So begins The Hangman's Daughter-the chillingly detailed, fast-paced historical thriller from German television screenwriter, Oliver Pötzsch-a descendent of the Kuisls, a famous Bavarian executioner clan.
A Map of the World
by Jane Hamilton
One unremarkable June morning, Alice Goodwin is, as usual, trying to keep in check both her temper and her tendency to blame herself for her family's shortcomings. When the Goodwins took over the last dairy farm in the small Midwestern town of Prairie Center, they envisioned their home a self-made paradise. But these days, as Alice is all too aware, her elder daughter Emma is prone to inexplicable fits of rage, her husband Howard distrusts her maternal competence, and Prairie Center's tight-knit suburban community shows no signs of warming to "those hippies who think they can run a farm."
A loner by nature, Alice is torn between a yearning for solitude coupled with a deep need to be at the center of a perfect family. On this particular day, Emma has started the morning with a violent tantrum, her little sister Claire is eating pennies, and it is Alice's turn to watch her neighbor's two small girls as well as her own. She absentmindedly steals a minute alone that quickly becomes ten: time enough for a devastating accident to occur. Her neighbor's daughter Lizzy drowns in the farm's pond, and Alice — whose own volatility and unmasked directness keep her on the outskirts of acceptance — becomes the perfect scapegoat. At the same time, a seemingly trivial incident from Alice's past resurfaces and takes on gigantic proportions, leading the Goodwins far from Lizzy's death into a maze of guilt and doubt culminating in a harrowing court trial and the family's shattering downfall.
How to Bake a Perfect Life
by Barbara O'Neal
In a novel as warm and embracing as a family kitchen, Barbara O'Neal explores the poignant, sometimes complex relationships between mothers and daughters — and the healing magic of homemade bread.
Professional baker Ramona Gallagher is a master of an art that has sustained her through the most turbulent times, including a baby at fifteen and an endless family feud. But now Ramona's bakery threatens to crumble around her. Literally. She's one water-heater disaster away from losing her grandmother's rambling Victorian and everything she's worked so hard to build.
When Ramona's soldier son-in-law is wounded in Afghanistan, her daughter, Sophia, races overseas to be at his side, leaving Ramona as the only suitable guardian for Sophia's thirteen-year-old stepdaughter, Katie. Heartbroken, Katie feels that she's being dumped again — this time on the doorstep of a woman out of practice with mothering.
Ramona relies upon a special set of tools — patience, persistence, and the reliability of a good recipe — when rebellious Katie arrives. And as she relives her own history of difficult choices, Ramona shares her love of baking with the troubled girl. Slowly, Katie begins to find self-acceptance and a place to call home. And when a man from her past returns to offer a second chance at love, Ramona discovers that even the best recipe tastes better when you add time, care, and a few secret ingredients of your own.
365 Thank Yous: The Year a Simple Act of Daily Gratitude Changed My Life
by John Kralik
One recent December, at age 53, John Kralik found his life at a terrible, frightening low: his small law firm was failing; he was struggling through a painful second divorce; he had grown distant from his two older children and was afraid he might lose contact with his young daughter; he was living in a tiny apartment where he froze in the winter and baked in the summer; he was 40 pounds overweight; his girlfriend had just broken up with him; and overall, his dearest life dreams-including hopes of upholding idealistic legal principles and of becoming a judge-seemed to have slipped beyond his reach. Then, during a desperate walk in the hills on New Year's Day, John was struck by the belief that his life might become at least tolerable if, instead of focusing on what he didn't have, he could find some way to be grateful for what he had. Inspired by a beautiful, simple note his ex-girlfriend had sent to thank him for his Christmas gift, John imagined that he might find a way to feel grateful by writing thank-you notes. To keep himself going, he set himself a goal-come what may-of writing 365 thank-you notes in the coming year. One by one, day after day, he began to handwrite thank yous-for gifts or kindnesses he'd received from loved ones and coworkers, from past business associates and current foes, from college friends and doctors and store clerks and handymen and neighbors, and anyone, really, absolutely anyone, who'd done him a good turn, however large or small. Immediately after he'd sent his very first notes, significant and surprising benefits began to come John's way-from financial gain to true friendship, from weight loss to inner peace. While John wrote his notes, the economy collapsed, the bank across the street from his office failed, but thank-you note by thank-you note, John's whole life turned around. 365 Thank Yous is a rare memoir: its touching, immediately accessible message-and benefits-come to readers from the plainspoken storytelling of an ordinary man. Kralik sets a believable, doable example of how to live a miraculously good life. To read 365 Thank Yous is to be changed.
Salting Roses
by Lorelle Marinello
A young woman abandoned as an infant on an Alabama porch is horrified to discover that she is the missing heiress to a vast Connecticut fortune — a birthright she is desperate to reject in favor of her Peachtree Lane roots.
Gracie Lynne Calloway — once left in a coal bucket on a front porch in a small Alabama town — discovers on her twenty-fifth birthday that she is the kidnapped daughter of a late New England financier and heiress to a fortune. When the tabloid press and her unwanted greedy relatives descend on her, she has to admit the quiet secure life she's known and loved is gone for good. As Gracie struggles to stabilize her world and come to terms with her new identity, she learns that belonging is not about where you came from but who you are.
An Object of Beauty
by Steve Martin
Lacey Yeager is young, captivating, and ambitious enough to take the NYC art world by storm. Groomed at Sotheby's and hungry to keep climbing the social and career ladders put before her, Lacey charms men and women, old and young, rich and even richer with her magnetic charisma and liveliness. Her ascension to the highest tiers of the city parallel the soaring heights-and, at times, the dark lows-of the art world and the country from the late 1990s through today.
by Walter Mosley
A masterful, moving novel about age, memory, and family from one of the true literary icons of our time.
Ptolemy Grey is ninety-one years old and has been all but forgotten-by his family, his friends, even himself-as he sinks into a lonely dementia. His grand-nephew, Ptolemy's only connection to the outside world, was recently killed in a drive-by shooting, and Ptolemy is too suspicious of anyone else to allow them into his life. until he meets Robyn, his niece's seventeen-year-old lodger and the only one willing to take care of an old man at his grandnephew's funeral.
But Robyn will not tolerate Ptolemy's hermitlike existence. She challenges him to interact more with the world around him, and he grasps more firmly onto his disappearing consciousness. However, this new activity pushes Ptolemy into the fold of a doctor touting an experimental drug that guarantees Ptolemy won't live to see age ninety- two but that he'll spend his last days in feverish vigor and clarity. With his mind clear, what Ptolemy finds-in his own past, in his own apartment, and in the circumstances surrounding his grand-nephew's death-is shocking enough to spur an old man to action, and to ensure a legacy that no one will forget.
In The Last Days of Ptolemy Grey, Mosley captures the compromised state of his protagonist's mind with profound sensitivity and insight, and creates an unforgettable pair of characters at the center of a novel that is sure to become a true contemporary classic.
The Wolves of Andover
by Kathleen Kent
In the harsh wilderness of colonial Massachusetts, Martha Allen works as a servant in her cousin's household, taking charge and locking wills with everyone. Thomas Carrier labors for the family and is known both for his immense strength and size and mysterious past. The two begin a courtship that suits their independent natures, with Thomas slowly revealing the story of his part in the English Civil War. But in the rugged new world they inhabit, danger is ever present, whether it be from the assassins sent from London to kill the executioner of Charles I or the wolves-in many forms-who hunt for blood. A love story and a tale of courage, The Wolves of Andover confirms Kathleen Kent's ability to craft powerful stories of family from colonial history.
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Isaac Barrow (Londres, octubre, 1630-Londres, 4 de mayo, 1677) fue un teólogo, profesor y matemático británico, cuyo papel en el desarrollo del cálculo moderno históricamente ha recibido un mérito secundario, en concreto, en su trabajo respecto a la tangente. Barrow es famoso por haber sido el primero en calcular las tangentes de la curva kappa. Isaac Newton fue discípulo de Barrow.

Biografía

Barrow nació en Londres. Él era el hijo de Thomas Barrow, un pañero de lino de oficio. En 1624, Thomas se casó con Ann, hija de William Buggin de North Cray, Kent, y su hijo Isaac nació en 1630. Parece que Barrow fue el único hijo de esta unión, sin duda el único hijo que sobrevivió a la infancia. Ann murió alrededor de 1634, y el padre viudo envió al muchacho a su abuelo, Isaac, el JP de Cambridgeshire, que residía en Spinney Abbey.  Sin embargo, dentro de dos años, Thomas se volvió a casar; la nueva esposa era Katherine Oxinden, hermana de Henry Oxinden de Maydekin, Kent. De este matrimonio, tuvo al menos una hija, Elizabeth (nacida en 1641), y un hijo, Thomas, que fue aprendiz de Edward Miller, desollador, y obtuvo su liberación en 1647, emigrando a Barbados en 1680.

Barrow empezó el colegio en Charterhouse (donde era tan agresivo y combativo que se cuenta que su padre rezaba a Dios para pedirle que, si algún día tuviera que llevarse a alguno de sus hijos, se llevara a Isaac). Completó su educación en el Trinity College, Cambridge, donde su tío y tocayo (más tarde obispo de St. Asaph), era Miembro de la Junta de Gobierno del colegio.

Fue muy estudioso, sobresaliendo especialmente en matemáticas; tras graduarse en 1648, le fue concedido un puesto de investigación en 1649. Residió unos cuantos años en Cambridge, y le fue ofrecido un puesto de profesor de Griego en su universidad, pero en 1655 fue expulsado debido a la persecución a la que era sometido por los independientes.

Los siguientes cuatro años estuvo viajando por Francia, Italia e incluso Constantinopla, y tras varias aventuras regresó a Inglaterra en 1659. Fue ordenado al año siguiente, así como nombrado profesor Regius de griego en Cambridge. En 1662 fue profesor de Geometría en el Gresham College, y en 1663 fue elegido primer profesor Lucasiano en Cambridge. Mientras ocupaba esta cátedra publicó dos trabajos matemáticos de gran profundidad y elegancia, el primero de ellos en Geometría y el segundo en Óptica. En 1669 dejó la cátedra en favor de su pupilo, Isaac Newton, quien fue considerado durante mucho tiempo el único matemático inglés que le ha superado. Durante este tiempo también escribió sus Expositions of the Creed, The Lord's Prayer, Decalogue, and Sacraments. El resto de su vida fue muy devota pues se dedicó al estudio de la teología. En 1672 fue director del Trinity College, donde fundó una biblioteca, que regentó hasta su muerte en Cambridge en 1677.

Además de los trabajos ya mencionados, escribió otros importantes tratados en matemáticas, pero en la literatura se dedicó especialmente a escribir sermones, que fueron obras maestras de argumentaciones elocuentes, donde su tratado Pope's Supremacy es considerado como uno de los tratados de controversia más perfectos que existen. Barrow como hombre fue en todos los aspectos digno de sus grandes talentos, aunque tuvo una gran vena excéntrica. Murió sin casarse en Londres a la temprana edad de 47 años.

Ha sido descrito como "bajo de estatura, flaco y de pálido aspecto", despreocupado en sus vestimentas y un empedernido fumador. Fue notoria su fuerza y valentía, y se cuenta que una vez cuando viajaba hacia el Este logró esquivar el ataque de unos piratas gracias a su destreza. Su predisposición e ingenio le hicieron favorito de Carlos II de Inglaterra, quien indujo a sus cortesanos a respetarle aunque no le mostraran aprecio. Escribía muy a menudo y con elocuencia, y con su intachable vida y su escrupulosa conciencia fue uno de los personajes más impresionantes de su tiempo.

Cálculo de tangentes
Las lecciones geométricas contienen algunas formas nuevas de determinar las áreas y las tangentes de las curvas. La más célebre de ellas es el método dado para la determinación de tangentes a curvas, y esto es lo suficientemente importante como para requerir una nota detallada, porque ilustra la forma en que Barrow, Hudde y Sluze estaban trabajando en las líneas sugeridas por Fermat hacia los métodos del cálculo diferencial.

Fermat había observado que la tangente en un punto "P" de una curva se determinaba si se conocía otro punto además de "P"; por lo tanto, si se pudiera encontrar la longitud de la subtangente MT (determinando así el punto T), entonces la línea TP sería la tangente requerida. Entonces Barrow comentó que si se dibujaban la abscisa y la ordenada en un punto Q adyacente a P, obtenía un pequeño triángulo PQR (que llamó el triángulo diferencial, porque sus lados QR y RP eran las diferencias de las abscisas y ordenadas de P y Q), de modo que
K
TM : MP = QR : RP.

Para encontrar QR : RP supuso que x, y
fueron las coordenadas de P, y x − e, y
− a los de Q (Barrow en realidad usó p para x y m para y, pero este artículo usa la notación moderna estándar) . Sustituyendo las coordenadas de Q en la ecuación de la curva, y despreciando los cuadrados y potencias superiores de e y a en comparación con sus primeras potencias, obtuvo e : a. La relación a/e fue posteriormente (de acuerdo con una sugerencia hecha por Sluze) denominada el coeficiente angular de la tangente en el punto.

Barrow aplicó este método a las curvas
x2 (x2 + y2) = r2y2, la curva kappa;
x3 + y3 = r3;
x3 + y3 = rxy, llamado la galande ;
y = (r − x) tan πx/2r, la cuadratriz; y
y = r tan πx/2r.

Aquí será suficiente tomar como ilustración el caso más simple de la parábola y2 = px.
Usando la notación dada arriba, tenemos para el punto P, y2 = px; y para el punto Q:
(y − a)2 = p(x − e).

Restando obtenemos
2ay − a2 = pe.
Pero, si a es una cantidad infinitesimal,
a2 debe ser infinitamente menor y por lo tanto puede despreciarse
cuando se compara con las cantidades 2ay y pe. Por eso
2ay = pe, es decir e : a = 2y : p.
Por lo tanto,
TM : y = e : a = 2y : p.
Por eso
TM = 2y2/p = 2x.

Este es exactamente el procedimiento del cálculo diferencial, excepto que allí
tener una regla por la cual podemos obtener la relación a/e o dy/dx directamente sin el trabajo de realizar un cálculo similar al anterior para cada caso por separado.

Realizaciones

Su primer trabajo fue una edición completa de los Elementos de Euclides, que fue editado en latín en 1655 y posteriormente en inglés en 1660; en 1657 publicó una edición de Datos. Sus lecturas, publicadas en 1664, 1665 y 1666, fueron más tarde reeditadas en 1683 bajo el título de Lecciones Matemáticas (en latín Lectiones Mathematicae); la mayoría hablan de fundamentos de metafísica para verdades matemáticas.

Sus lecturas de 1667 fueron publicadas el mismo año, y hablan del análisis sobre cómo Arquímedes pudo llegar a los resultados que obtuvo. En 1669 publicó sus Lectiones Opticae et Geometricae en el que se aproxima al actual proceso de diferenciación al determinar tangentes a curvas y estableció que la derivación y la integración son procesos inversos. Se dice en el prefacio que el propio Newton revisó y corrigió personalmente estas lecturas, añadiendo ideas propias, pero parece probable que los comentarios de Newton solo se refirieron a aquellas partes que hablan de los tratados de óptica. Este trabajo, que es su realización más importante en matemáticas, volvió a ser publicado con algunas pequeñas modificaciones en 1674. En 1675 publicó una nueva edición con numerosos comentarios de los primeros cuatro libros de On Conic Sections de Apolonio de Perge, y de otros trabajos de Arquímedes y de Teodosio.

Reconocimientos
 La Regla de Barrow, denomina con su nombre.
 El cráter lunar Barrow lleva este nombre en su honor.

Lecturas relacionadas
 W. W. Rouse Ball. A Short Account of the History of Mathematics (4th edition, 1908)
 Carl B. Boyer. Historia de la matemática (Alianza Editorial, 2010, Madrid) ISBN 9788420681863. Página 487-489 (de 808). Capítulo XVIII: Un período de transición.

Referencias

Enlaces externos

 The Master of Trinity at Trinity College, Cambridge

Matemáticos de Inglaterra del siglo XVII
Miembros de la Royal Society
Nacidos en Londres
Fallecidos en Londres

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text:
In the Trans-Siberian
By Sleigh to Tobolsk
Tobolsk Impressions
A Winter in Captivity
The Shadow of Coming Events
The Long Arm of Moscow
Journey to Ekaterinburg
Three Weeks in a Refugee Train
Under Bolshevik Rule
The Pendulum Swings Round
The American Hospital
The Kolchak Government
On Board the British Military Train
HAD I been told in January 1917 that the year would see me an exile in Siberia, completely cut off from my people, penniless, drifting from place to place, often in fear of my life, I should have thought the idea preposterous. I was at that time lady-in-waiting to the Empress Alexandra Feodorovna of Russia and was living with the Imperial Family at the Tsarskoe Selo Palace. I had many friends and no material anxieties. My parents were in Denmark, where my father was the Russian Minister. My busy life was pleasant, the Empress and her daughters were wonderfully kind to me. My two colleagues, the other ladies-in-waiting, were real friends. Though during the preceding two years rumours of smouldering political unrest in the country had added to the anxieties and suspense caused by the war, the approach of a tragedy unparalleled in history did not seem possible.
In March 1917 the Russian revolution broke out and the Emperor abdicated, and for five months, as a voluntary State prisoner, I shared the Imperial Family's imprisonment at the Tsarskoe Selo Palace. When the Kerensky Government decided to remove the Emperor and his family to "an unknown destination," which proved to be Tobolsk in Siberia, I was unable to accompany them, as I had to undergo an operation for appendicitis. I managed, however, to extract a promise from the authorities that I might join the Imperial Family on my recovery.
My convalescence lasted longer than was expected, but at last the day came when I could make preparations to start on my long journey. I little knew how long, nor how uncomfortable it was to be. In any case this was to me a matter of indifference, as my one desire was to rejoin the Emperor and Empress in their captivity. It took weeks to get the necessary permits to allow me to leave Petrograd at all. I obtained the final papers from the Kerensky Government on the very last day of its existence. On the next, November 7, the Bolshevik revolution broke out. This stopped all railway communication for several weeks and rendered my journey more difficult and even dangerous. The papers I had got with such trouble were no longer valid and I had no hope of obtaining others from the Bolsheviks, who would certainly have arrested me had I shown myself to them. My journey to Tobolsk had therefore to be a secret undertaking, for the Bolsheviks would have been quick to suspect a Monarchist plot if they heard of people going out to join the deposed Emperor. The Kerensky Government was still recognised in Siberia, and I knew that once I got there the permits I had would still hold good.
I was accompanied on my journey by my faithful old friend Miss A. D. Mather. She had been my mother's friend and companion since her earliest girlhood, and as soon as my nursery days were over she became my governess and was like a second mother to me. Miss Mather had stayed with my parents in Copenhagen after I left Russia to become the Empress's lady-in-waiting, and now, my mother having died, had come to Petrograd to be with me during my operation. She was a wonderful woman, always keeping her own distinct individuality in any surroundings, and the most true and understanding of friends. I tried to suggest to her that neither the journey to Siberia nor conditions of life there were suitable for a foreigner, especially to a woman of sixty, but she brushed aside all my objections. I could not go on such a journey alone, and if I went she would go with me. The way in which this quiet little old Scotch lady adapted herself to the most difficult situations was little short of marvellous. Though she was slight and delicate looking she had an iron determination and perfect self-command. She held her own before even the fiercest Bolshevik, never letting herself be hampered by her very bad Russian. Her keen sense of humour helped her to see the worst trials in the light of an amusing adventure and she would not allow herself to dwell too longingly on the thought of her beloved Scotland. Naturally the comfort of her sympathetic presence meant all the difference in the world to me.
In order not to disclose my identity, an acquaintance in Petrograd kindly volunteered to get us some railway tickets, and one evening in December he actually brought me three sleeping-car vouchers for next day. He had got them with much difficulty, and each was issued for a different town far up on the Trans-Siberian line, for, on his advice, in order to disarm suspicion. Miss Mather and my maid were to pretend to be fellow-travellers meeting by chance. We hurriedly made our last preparations and on the momentous day arrived at the station, separately, in accordance with the parts we had to play. The Petrograd station was in a state of indescribable chaos. As soon as passenger trains were run again, all those who could possibly do so fled from Petrograd to the provinces where Bolshevik rule was not as yet generally recognised. All time-tables had been done away with, and every traveller, with his family and all his belongings, sat for long hours in the waiting-room till the train he intended to go by eventually started. In these democratic times there were of course no porters. Some brave souls, who had risked being compromised by associating with us, had come to see us off, and they lent a willing hand. There was great difficulty in getting into the train at all, for the current axiom that "might is right" was applied here. When the signal to leave was given a general stampede took place. All the passengers rushed on to the platform and into the train, each one taking up at least twice the room he shouldhave done, for all had to carry for themselves the numberless bags and bundles of which my travelling countrymen are so fond. Lucidly some eventually got out again. They did not intend to go to Siberia at all and had only forced their way into the carriages in order to inquire about the train's destination. There was an awful moment when we three were finally settled in a compartment of the Trans-Siberian. A sailor, now evidently a high railway official, came to look through our papers. (No one was allowed to leave Petrograd at the time without special permit.) He seemed to belong to the crew of the Imperial yacht and might have recognised me, but luckily it was quite dark in the carriage and he was so much absorbed in Miss Mather's papers and studied her English passport so intently that he had no time to look at mine. It was fortunate, for this document was my old diplomatic passport with the Imperial arms and Monsieur Sazonoff's own signature!
The journey to Tyumen, the junction for Tobolsk, was supposed to take four days. Thence we were to have a drive of two hundred miles to Tobolsk itself. Our expectations were doomed to bitter disappointment, as the railway journey alone was to last nine days! This was the last month during which the "Trans-Siberian de luxe" was run, and even now nothing in the train's appearance conveyed the idea of luxury. All the coverings of the seats had been ripped off by our predecessors for their private use. In order to prevent the horsehair from appearing, dirty canvas covering had replaced the plush. Many of the windows were broken, all the brass bolts were missing, the water in the dressing-room did not run, and the whole carriage had evidently seen much ill-treatment.
After the train had started, a man in ragged clothes who proved to be the guard brought us a candle as a great luxury! By its light we discovered that we had a fourth occupant of our compartment in the shape of a lean young man with a strong likeness to Maxim Gorky. He wore a peasant's black shirt and high boots, a style of dress much affected in those times, and was deep in a number of one of the most extreme Communistic dailies. At first he scowled at us from behind his paper, but though civility was certainly not the fashion then, he gradually unbent and offered to take one of the upper berths. Owing to the difficulty of leaving the compartment he spent the greater part of the journey on the top of his shelf, reading his papers, the violence of whose opinions he seemed to appreciate. "Good stuff, this," we heard him remark. "This is strongly put." He lived on stale black bread which he extracted from a nondescript bundle, and most obligingly got out from time to time at the stations to fill our huge kettle with hot water. People versed in Siberian travel had made us invest in this, and it was a boon, as for many days we had to live mainly on tea.
When we left Petrograd there were only a few passengers sitting in the corridors. (Every compartment was, of course, over-filled.) The next morning, however, at Vologda, where the Moscow line joins the Siberian, the train was literally stormed by soldiers returning from the front. These men had left their units without the sanction of any authority. The army was in full dissolution. After the revolution of March 1917 a violent pacifist propaganda had been carried on in the trenches, and after the November upheaval the last vestiges of discipline had disappeared. The men swarmed in, carrying the most extraordinary luggage of every kind of article crammed into canvas bags and pillow-cases, or made up into bundles. They completely blocked up the corridors, and sat not only on the end platforms of the coaches but on the buffers. They clung to the steps outside, sat and stood in the dressing-rooms and, in short, pervaded everything, filling the carriages with the noise of their brawls. They were nearly all the class of soldier that we had seen in the streets of Petrograd during the last months. Their luggage showed what their occupation had been. They were carrying all the loot they had amassed during their stay in the capital, as well as all the firearms that they had been able to take with them on leaving the front. Out of their bundles protruded brass candlesticks, china, pieces of stuff, as well as every possible kind of weapon. In addition some of them carried one or two rifles under their arms, and at every man's belt hung a revolver or a dagger, or a couple of hand grenades. Among them were a few of a milder appearance, poor fellows, wounded or maimed, who were being invalided home from some hospital. These kept away as much as they could from the others, and stood silently huddled together, shoulder to shoulder, like sheep in a pen, for long hours at a stretch. Soon the men in the corridors forced themselves into the compartments. Luckily for us, we had only some of the wounded soldiers in ours, and even these left us in the course of the night. On the second morning we reached Viatka and after this travelled on at a snail's pace, losing and gaining hundreds of passengers at every station. At each stop the soldiers rushed out in a body to throw themselves on the food stalls, which displayed more and more provisions as we got further from Petrograd. Other soldiers forced their way in, and many of those who got out were never able to return. This was nearly my own fate. I too got out to buy some bread, and when I tried to force my way back into the carriage I found it was utterly impossible. Dozens of men were already clinging to the steps and showed no inclination to make way. My travelling companions and all my belongings, including my papers, were inside and it was vital for me not to be parted from them. One of the men suggested that I should be helped "up," as "a few fellows were already up there." I did not quite realise what "up there" meant and was not a little horrified when I found myself being hoisted by obliging hands on to the roof of the carriage! Here two soldiers were already reclining. I clamoured to be taken down, but the train had started and I had just to cling to the ventilator with all my might. The slowness of the train's progress was my salvation. Its rate was about sixteen miles an hour, but it seemed to me an endless time before we reached the next station. The carriage roof was domed and slippery. I sat astride the ventilator, clinging on with both hands, but at every curve of the line I felt I was gliding off. Luckily we passed under no bridges and it was only about zero P., a mild temperature for those parts. My two travelling companions gave me useful advice, but seemed to think me hopeless as a roof-traveller! It was they who asked their comrades to help me to get inside the train, saying with a friendliness born of having shared the same plight, "We must get her down or we shall lose her on the way." My relief at being once more inside our carriage can be imagined. I must honestly own that I had never been so much frightened in my life. I had always been particularly bad at gymnastics of any kind, and I believe it was sheer desperation that enabled me to overcome the awful giddiness caused by my "exalted" position.
Between Viatka and Perm we locked our door at night against the invasion of newcomers, for the last contingent seemed specially militant. Eventually they hammered loudly on the doors of all the shut compartments, demanding an entrance and threatening "death to the bourgaui." Some of the travellers opened the doors of their compartments, and the number of occupants was immediately increased to such an incredible extent that every one had, literally, a soldier sitting on his or her knee. On the advice of our "Gorky" we four pretended to snore loudly, to make the men outside think that the place was full of heavy sleepers. Happily they did not break open the door to investigate, and contented themselves with banging on the panels, shouting "Wake up, bourgaui!" alternating this with threats of hanging, murder, etc., the whole seasoned with the most forceful language. Next morning, when we tried to get out we found to our horror that this was an utter impossibility. The door was completely jammed by the compact mass of soldiers standing shoulder to shoulder in the corridor, and the handle could not be moved more than an inch or so. We had to remain prisoners in our coupe for nearly twenty-four hours, reduced for food to the young man's black bread, and for drink to some tea I had in a thermos flask.
We were beginning to get uneasy as to how the journey would end, when an incident occurred which seemed at first alarming, but which turned out better than we expected. The principles of equality now in force insisted that no one train could travel faster than any other. Ours was still officially an express - the extra fare being scrupulously charged - but had to crawl along at a snail's pace, as the military train in front of it objected to being outstripped. This greatly irritated our twaristchi (comrade soldiers), who sent a message to our engine-driver, threatening to shoot him if he did not increase his speed. He pointed out that there was a train just ahead, and this pacified the soldiers for a time, though they made up their minds to overtake their rival at the very first opportunity. In that land of freedom everyone considered that he had the right to regulate the movements of trains as well as of everything else.
The welcome opportunity arose very soon. The engine of the military train broke down and it had to stop at a station for a new one. On board this train was a detachment of Cossacks who had, wonderfully enough, kept some spirit of discipline and military tradition. For some private reason of their own they sounded a bugle which seemed acutely to irritate the nerves of our fellow-travellers. After a short discussion they made up their minds that the Cossacks were "old regime." Their new engine could be requisitioned as a punishment for their political opinions, and two engines would ensure an increase of speed to our train. This was no sooner said than done. Our soldiers poured out on to the platform, and while one party rushed towards the coveted engine, the other invaded the station-master's office in order to force him to give the necessary orders for the change. When the Cossacks realised what was going to be done they also got out of their train. Soon the sounds of shouting and of violent altercations filled the air. The Cossacks crowded round their engine, vehemently protesting against giving it up. The other party retaliated by unearthing several machine-guns from their baggage and prepared for battle. A bugle was again sounded, with the result that a stream of Cossacks with rifles in hand poured out of the carriages to reinforce their comrades. Things seemed to be getting serious. Travellers "with experience of such incidents" tried to let down the windows, but these were frozen and jammed. This, it was explained to us, was a necessary precaution, for fear we should be cut by the splinters of glass when the firing began. Luckily, just as the signal for the first volley was given, our train began unexpectedly to move. Some of the soldiers had profited by the preparations for the fight to couple the much-desired engine on to our train. A terrible scurry ensued. A few of the men managed to jump in, but to our great joy the majority remained at the station. The corridors were less packed. We could at last get out of our compartment, though it was still difficult and elicited many oaths from the soldiery.
The Cossack incident was the theme of conversation and discussion all through the following day, and the bourgoui and their numerous crimes and defects were happily forgotten.
The soldiers' conversation was most instructive and gave an insight into their mentality at the time. One man, for instance, a real Bolshevik type, with abundant locks in picturesque disorder - a style of coiffure much admired in the Red Army � lamented loudly that most of his luggage had remained at the station where the Cossack incident had taken place. "This is my reward for having tired myself out beating the station-master," he said. "My arm is quite sore." The statement was received as a perfectly lawful grievance by his hearers, and was the cause of much sympathy. On the whole the mood of our travelling companions had improved. The most riotous element had remained at the momentous station and physical fatigue had quenched the warlike spirit of the rest. They profited by the increase of space to lie down, one on top of the other, wherever they could. They laid on the floors of the compartments and in the corridors; some even got on to the luggage racks. Many had come all the great distance from Poland and had probably travelled the whole way in the same conditions. They were so tired that they slept anywhere, standing, sitting on the ground, on their bags, never seeming even to feel their comrades when they stepped on them in trying to squeeze past.
For a long time I had noticed one man who was especially haggard and weary-looking. He had apparently stood out in the cold on the end platform for six whole days. He looked ill, his coat was old and tattered and his boots were worn out. He had no large bundles of loot and ate only dry bread washed down with a glass of tea when some of the others thought fit to ask him to join them at their meals. Silent and immovable, he leaned against the wall, the picture of patient misery. The others laughed at him, calling him the "lunatic" when he did not take part in their talk. I asked him why he was standing out in the cold, now that there was more room in the corridor. "I don't mind," he answered, "there will be an end to it soon. But I will not be with 'them " - jerking his thumb in the direction of the others. "They are 'possessed.' Nothing is sacred to them, and I would rather freeze than listen to their talk. I advise you, too, to keep clear of them. They have no conscience, they are evil men." So he remained aloof, and I always remember his plain, pock-pitted face, the patient look of the old Russian soldier in his eyes, and the sadness of the battlefield that seemed to be stamped all over him. He was certainly one of those who had really fought for his country during those tragic years, and not, like the rest, a product of the revolution.
The last two days of our train journey were uneventful. The crowded carriages had, in a way, proved a blessing to us, as they had prevented any examination of our papers by Kommissars on the way. Even Kommissars could not force themselves into the trains and no demand was made for our papers, which would have disclosed the object of our journey and would probably have led to our arrest. Now we were out of the zone of acute danger. After we had passed Ekaterinburg, the first town in the Ural region, the weather became milder and the window-panes clear again. We were able to see the scenery, wide expanses of forest covering the slopes and gradually rising towards the Ural Mountains.
We passed somewhere the well-known pillar on one side of which is inscribed "Europe" and on the other "Asia." We were at last in Siberia, that vast part of Russia so little known even to many Russians, where is found every kind of climate from the Polar cold to Southern heat in the Altai regions, and where advanced civilisation exists side by side with the primitive conditions of old-world life.
A special thank you to tess224@yahoo.com for scanning the text for this online edition.
Contact Bob Atchison for comments on this site.
Other books on Russian History from the Alexander Palace Association:
The Life and Tragedy of Alexandra Feodorovna by Sophie Buxhoeveden | Memories of the Russian Court by Anna Vyrubova | Thirteen Years at the Russian Court by Pierre Gilliard | Last Days at Tsarskoe Selo by Paul Beckendorff | St. Petersburg - Imperial City | Charles Cameron - Imperial Architect by Georges Loukomski | Tsarskoe Selo in 1910
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