## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 93

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**scholium**is a remark on one or several preceding propo- sitions , which tends to point out their connexion , their use , their restriction , or their extension . A hypothesis is a supposition , made either in the enunciation of a ... Page 16

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**Scholium**. The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the ... Page 17

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**Scholium**. Two triangles are said to be equal , when being applied to each other , they will exactly coincide ( Ax . 13. ) . Hence , equal triangles have their like parts equal , each to each , since those parts must coincide with each ... Page 19

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**Scholium**. Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of the triangle EDF , each to each , while the third side BC of the first triangle is greater than the third side EF of the second ... Page 20

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**Scholium**. It may be observed that the equal angles lie op- posite the equal sides : thus , the equal angles D and A , lie op- posite the equal sides EF and BC . PROPOSITION XI . THEOREM . " " In an isosceles triangle , the angles ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex