## Elements of Geometry and Trigonometry |

### From inside the book

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**propositions**of Geometry are general truths , and as such , should be stated in gene- ral terms , and without reference to particular figures . The method of enunciating them by the aid of particu- lar diagrams seems to have been ... Page 12

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**proposition**, is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several**propositions**. A scholium is a remark on one or several preceding propo- sitions , which ... Page 14

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**PROPOSITION**II . THEOREM .. Two straight lines , which have two points common , coincide with each other throughout their whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place ... Page 15

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**PROPOSITION**III . THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two straight lines which are met , will form one and the same ... Page 17

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**PROPOSITION**VI . THEOREM . If two triangles have two angles and the included side of the one , equal to two angles and the included side of the other , each to each , the two triangles will be equal . Let the angle E be equal to the ...### 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