Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 100
Page 12
... theorem , or the solution of a problem . The common name , 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 ...
... theorem , or the solution of a problem . The common name , 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 ...
Page 14
... 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 it is evident ...
... 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 it is evident ...
Page 15
... 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 straight line . Let ...
... 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 straight line . Let ...
Page 18
... THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short ...
... THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short ...
Page 19
... theorem , AG + GC AB + BC ; and , taking AG from the one , and its equal AB from the other , there will remain GC < BC or BC > EF . B Scholium . Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of ...
... theorem , AG + GC AB + BC ; and , taking AG from the one , and its equal AB from the other , there will remain GC < BC or BC > EF . B Scholium . Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of ...
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex