## The Elements of Euclid, with many additional propositions, and explanatory notes, by H. Law. Pt. 2, containing the 4th, 5th, 6th, 11th, & 12th books1855 |

### From inside the book

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**triangles have an angle of the one equal to an angle of the other**, they are to one another as the rectangles under the sides about those angles . COROLLARY 2. If triangles and parallelograms are equiangular , they are to one another as ... Page 196

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**triangles have an angle of the one equal to an angle of the other**. If triangles are equiangular . If triangles are similar If equal**triangles have an angle of the one equal to an angle of the other**. If triangles have an angle in the ...### Other editions - View all

The Elements of Euclid: With Many Additional Propositions, & Explanatory ... Euclid No preview available - 2023 |

The Elements of Euclid: With Many Additional Propositions, and Explanatory ... Euclid No preview available - 2013 |

### Common terms and phrases

algebraically expressed altitude angle ABC angle BAC axis base ABC base DEF base EH circle ABCD circle EFGH circumference common section cone contained COROLLARY cylinder DEMONSTRATION diameter divided duplicate ratio equal and similar equal angles equi equiangular equimultiples Euclid ex æquali fore four magnitudes fourth given circle given straight line gnomon greater ratio homologous sides Hypoth inscribed join less meet multiple opposite planes paral parallel parallelogram pentagon perpendicular polygon prism PROPOSITION pyramid ABCG pyramid DEFH reciprocally proportional rectangle rectilineal figure remaining angle right angles SCHOLIUM segments solid angle solid CD solid parallelopipeds solid polyhedron square on BD THEOREM THEOREM.-If third three plane angles tiple triangle ABC triplicate ratio vertex vertex the point wherefore

### Popular passages

Page 198 - ... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another.

Page 75 - ... if the segments of the base have the same ratio which the other sides of the triangle have to one another...

Page 115 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 82 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.

Page 198 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 53 - Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth.

Page 40 - A and B are not unequal ; that is, they are equal. Next, let C have the same ratio to each of the magnitudes A and B ; then A shall be equal to B.

Page 119 - For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK.

Page 115 - FB ; (i. 4.) for the same reason, CF is equal to FD : and because AD is equal to BC, and AF to FB, the two sides FA, AD are equal to the two FB, BC, each to each ; and the base DF was proved equal to the base FC ; therefore the angle FAD is equal to the angle FBC: (i. 8.) again, it was proved that GA is equal to BH, and also AF to FB; therefore FA and AG are equal...

Page 94 - C, they are equiangular, and also have their sides about the equal angles proportionals (def. 1. 6.). Again, because B is similar to C, they are equiangular, and have their sides about the equal angles proportionals (def. 1. 6.) : therefore the figures A, B, are each of them equiangular to C, and have the sides about the equal angles of each of them, and of C, proportionals. Wherefore the rectilineal figures A and B are equiangular (1. Ax. 1.), and have their sides about the equal angles proportionals...