| Euclides - 1865
...the equal angles reciprocally proportional, are equal to one another. Prop. 15. Equal triangles which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional : and conversely, triangles which... | |
| James Robert Christie - Mathematics - 1866 - 404 pages
...of the other, have their sides about the equal angles reciprocally proportional; and triangles which **have one angle of the one equal to one angle of the other, and their** sides about the equal angles reciprocally proportional, are equal. 6. The circumferences of circles... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...and shall have those angles equal about which the sides are proportionals. Let the triangles ABC, DEF **have one angle of the one equal to one angle of the other,** namely, the angle BA C equal to the angle EDF, and the sides about two other angles ABC, DEF, proportionals,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham **one angle of the one equal to one angle of the other,** have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate... | |
| James Maurice Wilson - Geometry - 1868
...of a pair of corresponding sides involves the identity of the triangles. THEOREM 7. If two triangles **have one angle of the one equal to one angle of the other; and** the sides about the equal angles proportionals, then will the triangles be similar. Let the triangles... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880
...the segments BG, GD, GC of the base shall be in harmonical proportion. 12. Equal parallelograms which **have one angle of the one equal to one angle of the other** have their sides about the equal angles reciprocally proportional. ALGEBRA. 1. Prove that se и х... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...parallelogram BC. [V. 9. Wherefore, equal parallelograms &c. QED PROPOSITION 16. THEOREM. Equal triangles which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional; and triangles which have one angle... | |
| GEORGE BRUCE HALSTED - 1881
...both sides of a rectangle from their ratio m : n, and its area R. \mR Ans. n \ m 521. If two triangles **have one angle of the one equal to one angle of the other, and** the sides about a second angle in each equal, then the third angles will be either equal or supplemental.... | |
| Education, Higher - 1883
...proportion. When is a straight line said to be cut in extreme and mean ratio ? 14. Equal triangles which **have one angle of the one equal to one angle of the other,** have their sides about the equal angels reciprocally proportional ; and triangles which have one angle... | |
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