Why the intersections at n being composed of two compound derived shadows, forms a compound shadow and not a simple one, as happens with other intersections of compound shadows. This occurs, according to the 2nd [diagram] of this [prop.] which says:—The intersection of derived shadows when produced by the intersection of columnar shadows caused by a single light does not produce a simple shadow. And this is the corollary of the 1st [prop.] which says:—The intersection of simple derived shadows never results in a deeper shadow, because the deepest shadows all added together cannot be darker than one by itself. Since, if many deepest shadows increased in depth by their duplication, they could not be called the deepest shadows, but only part-shadows. But if such intersections are illuminated by a second light placed between the eye and the intersecting bodies, then those shadows would become compound shadows and be uniformly dark just as much at the intersection as throughout the rest. In the 1st and 2nd above, the intersections i k will not be doubled in depth as it is doubled in quantity. But in this 3rd, at the intersections g n they will be double in depth and in quantity.


First Book: What Book Got You Hooked?
I can't say I'm surprised by anything on that list – the Nancy Drew books were among my childhood favorites, and the Little House series and Alcott's works grace my shelves even today, but I have to confess that I wish fewer people were introduced to reading by Dr. Seuss, but that's my bias, because I've never been a fan of his sing-songy style.
For the rest of the top 50, go here.


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Australia aims for World Cup 'shock' against Argentina
Australia's Milos Degenek celebrates his team victory during the World Cup group D soccer match between Australia and Denmark, at the Al Janoub Stadium in Al Wakrah, Qatar, Wednesday, Nov. 30, 2022. (AP Photo/Darko Vojinovic) Credit: AP/Darko Vojinovic
By The Associated Press December 1, 2022
DOHA, Qatar — Australia center forward Mitchell Duke plays in the Japanese second division. Midfielder Ajdin Hrustic of Hellas Verona — the last-placed team in Italy's Serie A — is the team's lone player based in Europe's top five leagues.
After unexpectedly surviving the World Cup group stage, the Socceroos will once again rely on team work, determination and self-belief when they go up against star-studded Argentina in the round of 16.
"We have no real pressure," said forward Mathew Leckie, who scored in a 1-0 win over Denmark. "We just need to enjoy the moment, enjoy the occasion. No one expects us to win. So let's shock the world."
Center back Harry Souttar, the man who will be charged with stopping Lionel Messi in Australia's next match, is the tallest outfield player at the World Cup at 6-foot-6 (1.98-meters).
He only recently returned from ACL surgery but his and the team's confidence has been building game after game while advancing from a difficult group featuring defending champion France and European Championship semifinalist Denmark.
"It's 11 against 11. There's not 11 Messis. There is one," right back Milos Degenek said Thursday. "We know their squad is full of full of stars. Even (Paulo) Dybala is on the bench and (Lautaro) Martinez comes off the bench. So it's a squad that's immaculate.
"I always loved Messi, and I think he's the greatest to ever play the game," Degenek added. "(But) it's not an honour to play against him, because he's just a human, as we all are."
Australian soccer fans celebrate a goal scored as they watch the World Cup group D soccer match between Australia and Denmark, at the Al Janoub Stadium in Al Wakrah, Qatar, at Federation Square in Melbourne, Australia, in the early hours of Thursday, Dec. 1, 2022. Australia will play Argentina in a round of 16 match on Saturday, Dec. 3. (Con Chronis/AAP Image via AP) Credit: AP/Con Chronis
Australia's performance has been a testament to team spirit and proving doubters wrong.
"No one believed in us apart from us and the people around us," Degenek said Thursday. "So it's phenomenal."
It's only the second time in six World Cups that Australia has reached the knockout stage. The 2006 team was beaten by eventual champion Italy in the round of 16 on a controversial stoppage-time penalty.
Australia only qualified for this tournament following a penalty shootout win over Peru in an intercontinental playoff in June. But planning for the World Cup started long before that.
Australia's Mitchell Duke heads the ball during the World Cup group D soccer match against Denmark, at the Al Janoub Stadium in Al Wakrah, Qatar, Wednesday, Nov. 30, 2022. (AP Photo/Aijaz Rahi) Credit: AP/Aijaz Rahi
Degenek left Red Star Belgrade in January for the Columbus Crew in MLS, specifically to get more playing time in view of the tournament in Qatar.
Duke, who scored with a difficult header in Australia's 1-0 win over Tunisia, once considered becoming an electrician when his soccer career stalled. Then coach Graham Arnold gave him a chance with Central Coast Mariners and the pair are now reunited with Australia.
"Obviously I've got a lot of faith in the kid," Arnold said. "Everyone talks about where he plays but when he walks over that white line he gives 100% for the nation and the jersey."
Andrew Dampf is at https://twitter.com/AndrewDampf
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