Elements of Geometry and Trigonometry |
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Page 23
... draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the ... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ...
... draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the ... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ...
Page 24
... drawn , one of these lines will cut the perpendicular in D ; from which , drawing DB , we shall have DB DA . But the ... draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side BA ...
... drawn , one of these lines will cut the perpendicular in D ; from which , drawing DB , we shall have DB DA . But the ... draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side BA ...
Page 25
... draw the straight line EGF , perpendicular to EC . It will also be perpendicular to BD . For , the sum BAC + ABD is equal to two right angles , by hypothesis ; the sum BAC + BAE is likewise equal to two right angles ( Prop . I. ) ; and ...
... draw the straight line EGF , perpendicular to EC . It will also be perpendicular to BD . For , the sum BAC + ABD is equal to two right angles , by hypothesis ; the sum BAC + BAE is likewise equal to two right angles ( Prop . I. ) ; and ...
Page 28
... Draw PQR perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be perpendicular to AB ... drawn perpendicular to AB , these straight A lines will at the same time be T E perpendicular to CD ( Prop . XX . Cor ...
... Draw PQR perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be perpendicular to AB ... drawn perpendicular to AB , these straight A lines will at the same time be T E perpendicular to CD ( Prop . XX . Cor ...
Page 29
... draw AE parallel to BC . Then , since AE , CB , are parallel , and CAD cuts them , the exterior angle DAE will be equal to its inte - C rior opposite one ACB ( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel , and ...
... draw AE parallel to BC . Then , since AE , CB , are parallel , and CAD cuts them , the exterior angle DAE will be equal to its inte - C rior opposite one ACB ( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel , and ...
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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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex