| Robert Simson - Trigonometry - 1806 - 546 pages
...angles reciprocally proportional : and parallelograms that have one angle of the ono» equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Let AB, BC be equal parallelograms, which have the angles at B equal, and... | |
| John Playfair - Mathematics - 1806 - 320 pages
...equal angles reciprocally proportional ; and parallelograms which have one angle of one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Let AB, BC be equal parallelograms, which have the angles at B equal ; the... | |
| Euclides - 1816 - 588 pages
...equal angles reciprocally proportional: And parallelograms that have one angle of the one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one anothfen Let AB, BC be equal parallelograms, which have the angles at B equal, and... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...chord has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums **have an angle of the one equal to an angle of the other, and** if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Daniel Cresswell - Geometry - 1819 - 486 pages
...FAE, FH :HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVU. 23. THEOREM. If two trapeziums **have an angle of the one equal to an angle of the other, and** if, also, the sides of the two ^figures, about each of their angles, be proportionals, the remaining... | |
| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...general properties of triangles involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave **an angle of the one equal to an angle of the other and** the sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle A =... | |
| John Mason Good - 1819 - 800 pages
...angles reciprocally proportional : and parallelograms that iiive one angle of the one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Prop. XV. Theor. Equal triangles which have one angle of the one «qual to... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...angles reciprocally proportional : And parallelograms 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 to one another. Let AB, BC be equal parallelograms, which have the angles at B equal,, and... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...equal to the sum of the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which **have an angle of the one equal to an angle of the other,** are to each other as the rectangle of the sides about the equal Suppose* the two triangles joined,... | |
| Adrien Marie Legendre - 1825 - 570 pages
...: FH : : CD : HI ; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, **have an angle of the one equal to an angle of the other and** the sides about the equal angles proportional ; they are therefore similar (208). We might proceed... | |
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