Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 35
... drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ... draw the lines DA and DB . Then will DA and DB be equal ( P. XV . ) : hence , D is equally distant from A and D B ...
... drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ... draw the lines DA and DB . Then will DA and DB be equal ( P. XV . ) : hence , D is equally distant from A and D B ...
Page 36
... draw DB . Then , from what has just been shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and DB is equal to the sum of ID and DA , or IA , we have IB less than IA ...
... draw DB . Then , from what has just been shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and DB is equal to the sum of ID and DA , or IA , we have IB less than IA ...
Page 38
... KC and HD be parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it to E The sum of the angles GBE and GBD is equal to two right EB H- -D G K AF angles ( P. I. ) ; the sum of the 38 GEOMETRY .
... KC and HD be parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it to E The sum of the angles GBE and GBD is equal to two right EB H- -D G K AF angles ( P. I. ) ; the sum of the 38 GEOMETRY .
Page 42
... draw PR perpendicular to C EF ; then will it be perpendicular to AB , and also to CD ( P. XX . , C. 1 ) : hence , AB and CD are perpendicu- lar to the same straight line , and consequently , they are par- allel to each other ( P. XVIII ...
... draw PR perpendicular to C EF ; then will it be perpendicular to AB , and also to CD ( P. XX . , C. 1 ) : hence , AB and CD are perpendicu- lar to the same straight line , and consequently , they are par- allel to each other ( P. XVIII ...
Page 48
... Draw the diagonal DB . triangles ADB and CBD , will have D the sides of the one equal to the sides of the other , each to each ; and therefore , the triangles will be equal in all of their parts hence , the angle ABD is equal to the ...
... Draw the diagonal DB . triangles ADB and CBD , will have D the sides of the one equal to the sides of the other , each to each ; and therefore , the triangles will be equal in all of their parts hence , the angle ABD is equal to the ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence