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" ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2. "
The Elements of Euclid: In which the Propositions are Demonstrated in a New ... - Page 80
by Euclid - 1776 - 264 pages
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 520 pages
...alfo FB, BG are in one ftraight line1 : The fides of the parallelograms AB, BC about the equal angles, are reciprocally proportional ; that is, DB is to BE, as GB to BF. Complete the parallelogram FE ; and becaufe the parallelogram AB is equal to BC, and . ---- that FE...
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The Elements of Euclid,: In which the Propositions are Demonstrated in a New ...

Euclid - Geometry - 1776 - 318 pages
...at B equal ; and let the fides DB, BE, be in one right line, and FB, BG, in another; then the iides DB, BE, and GB, BF, that are about the equal angles...parallelogram AB is to EF, fo a 7. s- is BC to FE a; but, as AB is to FE, fo is the bafe DB to BE b; *^ '• and, as BC is ro FE, fo is GB to BF a ;...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 550 pages
...FB, BG are in one ftraight line * : The fides of the parallelograms AB, BC about the equal angles, are reciprocally proportional ; that is, DB is to BE, as GB to BF. Complete the parallelogram FE ; and becaufe the parallelogram AB is equal to BC, and that FE is another...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 444 pages
...are in one ftraight line» : the fides of the parallelograms AB, BC about the e- »14-jqual angles, are reciprocally proportional ; that is, DB is to BE, as GB to BF. Complete the parallelogram FE ; and becaufe the parallelogram AB is equal to BC, and that FE is another...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...FB, BG are in one ftraight line »..the fides of the parallelograms AB, BC about the equal angles, are reciprocally proportional ; that is, DB is to BE, as GB to BF. Complete the parallelogram FE; and becaufe the parallelogram AB is equal to BC, and that FE is another...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...are in one •14. 1. straight line". The sides of the parallelograms AB, BC about the equal angles, are reciprocally proportional; that is, DB is to BE, as GB to BF. Complete the parallelogram FE ; and because the parallelogram AB is equal to^ ~£ BC, and that FE is...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...are in one straight line (14. 1.) : the sides of the parallelograms AB, BC, about the equal angles, are reciprocally proportional ; that is, DB is to BE, as GB to BF. Complete the parallelogram FE ; and because the parallelograms AB, BC are equal, and F£ is another...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...are in one straight line (14. 1.) : the sides of the parallelograms AB, BC, about the equal angles, are reciprocally proportional ; that is, DB is to BE, as GB to V BF. Complete the parallelogram FE ; and because the parallelog AB, BC are equal, and FK is another...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...BG are in one itraight liner (14. 1.) The sides of the parallelograms AB, BC about the equal angles, are reciprocally proportional : that is, DB is to BE, as GB to BF. Complete the parallelogram FE ; and because the parallelogram AB is equal to ”1C, and that FE is another...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...BC be two equal parallelograms, which have the angles at B equal; the sides about the equal angles are reciprocally proportional, that is, DB is to BE as GB to BF. Let the sides DB, BE be placed in the same line, then the angles DBG, GBE are equal to two right angles ( 1...
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