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" BFE : (i. def. 10.) therefore, in the two triangles, EAF, EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other... "
Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ... - Page 90
by Euclides - 1840
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 pages
...the angle f. if. i. DTY is equal f to the angle GTS. therefore in the triangles DTY, GTS there are two angles in the one equal to two angles in the other, aid one fide equal to one fide, oppolite to two of the equal angles-, viz. DY to GS ; for they are...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...and the angle l)TY is equal f to the angle G PS : Therefore in the triangles D l"Y, GTS tlv;re are two angles in the one equal to two angles in the other, and one lide equal to one fide, oppofite to two of the equal angles, viz.. DY to GS ; for they are...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...equal c ; and the angle DTY is equal t to the angle GTS : Therefore in the triangles DTY, GTS there are two angles in the one equal to two angles in the other, and one fide equal to one^fide, oppofite to two of the equal angles, viz. DY to GSj for they arc the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...vertical angles AED, CEB are equal a, and alfo the alternate angles EAD, ECB b, the triangles ADE, CEB have two angles in the one equal to two angles in the other, each to each : but the fides AD arid BC, which are opppfite tp equal angles in thefe trier 34. i. angles,...
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The Economy of Nature Explained and Illustrated on the Principles ..., Volume 1

George Gregory - Philosophy - 1796 - 620 pages
...equal to GDC, QpM is equal to GDB but GDB is equal to MDq; in the two triangles QJD M, MD q, there are two angles in the one equal to two angles in the other, and one fide MD common to both, therefore QJM will be equal to My. The fame may be proved alfo of the...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...equal c ; and the angle DTY is equal f to the angle GTS. therefore in the triangles DTY, GTS there are two angles in the one equal to two angles in the other, and one fide equal to one fide, oppofite to two of the equal angles, viz. DY to GS; for they are the...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...the angle ABD to the angle CDB, and the angle ADB to the angle CBD. Hence the two triangles, having two angles in the one equal to two angles in the other, have also their third angles equal (cor. l,th. 17), namely, the angle A equal to the angle c, which...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...the angle ABD to the angle CDB, and the angle ADB to the angle CBD. Hence the two triangles, having two angles in the one equal to two angles in the other, have also their third angles equal (cor. 1, th. 17), namely, the angle A equal to the angle c, which...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...ADB and С В D are equal. Therefore the triangles BD С and DBA are identical, (Theo. 2.) ; having two angles in the one equal to two angles in the other, and the side BD between the equal angles, common to both; the triangle ABD is therefore equal to the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...and the angle DTY, is equal (IS. 1.) to the angle GTS : Therefore in the triangles DTY, GTS there are two angles in the one equal to two angles in the other, and one side equal to one side, opposite to two of the equal angles, viz. DY to GS ; for they are the...
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