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" If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let... "
The Elements of Euclid, containing the first six books, with a selection of ... - Seite 232
von Euclides - 1874
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 376 Seiten
...circle. PROPOSITION XXXI. THEOREM. (Eucl. vi. 32.) If two triangles, SIMILARLY SITUATED, which have two sides of the one proportional to two sides of...angle, so as to have their homologous sides parallel, each to each, the remaining sides must be in a straight line. Let the AS ABC, DCE be similarly situated,...
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Euclidian Geometry

Francis Cuthbertson - 1874 - 400 Seiten
...rectangle (FH, GS)+ rectangle (FH, SK) = rectangle (FH t GK). THEOREM (;'). If two triangles which have two sides of the one proportional to two sides of the other be joined at one angle, so as to have the former sides parallel to the latter respectively: the remaining sides shall be in a straight line....
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 Seiten
...therefore the triangles ABC and DEF are similar to each other, WWTBD Inversely If two triangles have two sides of the one proportional to two sides of the other, and if the angles formed by these sides be not equal to each other, the third sides of the triangles...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 Seiten
...described figures upon the sides containing the right angles. . . 240 32. If two triangles, which have two sides of the one proportional to two sides of the other, can be joined at one angle, so as to have their homologous sides parallel to one another, the remaining...
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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

James Hamblin Smith - 1879 - 378 Seiten
...circle. PROPOSITION XXXI. THEOREM. (Eucl. vi. 32.) If two triangles, SIMILARLY SITUATED, which have two sides of the one proportional to two sides of the other, tie joined at one angle, so as to have their homologous sides parallel, each to each, the remaining...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 Seiten
..."Wherefore, in any right-angled triangle &c. QED PROPOSITION 32. THEOREM. If two triangles, which have two sides of the one proportional to two sides of...remaining sides shall be in a straight line. Let ABC and DCE be two triangles, which have the two sides BA, AC proportional to the two sides CD, DE, namely,...
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Elements of Quaternions

Arthur Sherburne Hardy - 1881 - 248 Seiten
...МНР = PD + BP, m = 1, »i=l, and OP = PD, BP = PA. .. , j / ./?„,' 3. If two triangles, having two sides of the one proportional to two sides of...angle so as to have their homologous sides parallel, the remaining sides shall be in a straight line. Let (Fig. 9) AB = a, AE = ß. Then, ^ F1*- 9Ъу condition,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 Seiten
...demonstration or confirmation of that proposition. PROP. XXXII. THEOREM. If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, to at to have their homologous sides parallel to one another and proceeding from their vertices in...
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The Cambridge Examiner, Band 4

1884 - 538 Seiten
...point of contact shall be perpendicular to the line touching the circle. 14. If two triangles have two sides of the one proportional to two sides of the other, and the angles opposite to one pair of homologous sides equal, the angles which are opposite to the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 Seiten
..."Wherefore, in any right-angled triangle &c. QED PROPOSITION 32. THEOREM. If two triangles, which have two sides of the one proportional to two sides of...remaining sides shall be in a straight line. Let ABC and DCE be two triangles, which have the two sides BA, AC proportional to the two sides CD, DE, namely,...
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