Memoires 6
Memoires 6
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In our eReader you can find the full English version of the book. Read Memoires 6 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Memoires 6
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— Givm the angle ABC and the point P wi^hin it, to prove thaï the straight Une APG drawn Ihrough the point P will be a minimum when AP= GP', BP' being perpeiidicnlar to AC.
Proof by the i" Book of Euclid. — Complète the parallelo- gram ABCO (fig. 1); draw any othep line A'PG' through P;*then we hâve BG = OA, CP'=AP, and (1,27) ABCP'^AOAP.
.-. (1, 4) BP'=:OP and AAPO^ AP, which is a right A- .'.OP is perpendiculap to AG, and .•. it exceeds OP", perpendicular to A'PG^ Novv AAA'G' is > AAA'c, whic...h !s = AAA'O (I, 37).
Take each fpom OAA'G'; .-. AOA'C' > AAOG', which (by I, 37) is = AAOC. Thi^s AA'OG' basa greater area and a less altitude than AAOC, and .-. a fortiori A'G' > AG.
§11.
Theorem. — The middXe points of the ihree diagonals of a complète quadrilatéral ABGD lie in directum, The three diagonals are AG, BD and EF (Jig. 2); draw lines through B, G, D, E, F, parallel to the sides of A A; then (I, 43) thepapallelogramAG==GG,andal8o=:^GH; .-. A^K^rrA^L, .-.(by 164 GEOMETRICAL MISCELLANIES.
What to read after Memoires 6?
You can find similar books in the "Read Also" column, or choose other free books by Société Des Sciences Physiques Et Naturelles De Bordeaux to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
— Givm the angle ABC and the point P wi^hin it, to prove thaï the straight Une APG drawn Ihrough the point P will be a minimum when AP= GP', BP' being perpeiidicnlar to AC.
Proof by the i" Book of Euclid. — Complète the parallelo- gram ABCO (fig. 1); draw any othep line A'PG' through P;*then we hâve BG = OA, CP'=AP, and (1,27) ABCP'^AOAP.
.-. (1, 4) BP'=:OP and AAPO^ AP, which is a right A- .'.OP is perpendiculap to AG, and .•. it exceeds OP", perpendicular to A'PG^ Novv AAA'G' is > AAA'c, whic...h !s = AAA'O (I, 37).
Take each fpom OAA'G'; .-. AOA'C' > AAOG', which (by I, 37) is = AAOC. Thi^s AA'OG' basa greater area and a less altitude than AAOC, and .-. a fortiori A'G' > AG.
§11.
Theorem. — The middXe points of the ihree diagonals of a complète quadrilatéral ABGD lie in directum, The three diagonals are AG, BD and EF (Jig. 2); draw lines through B, G, D, E, F, parallel to the sides of A A; then (I, 43) thepapallelogramAG==GG,andal8o=:^GH; .-. A^K^rrA^L, .-.(by 164 GEOMETRICAL MISCELLANIES.
What to read after Memoires 6?
You can find similar books in the "Read Also" column, or choose other free books by Société Des Sciences Physiques Et Naturelles De Bordeaux to read onlineMoreLess
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