Elements of Geometry and Trigonometry |
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Page 26
... triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , measured on any broken line AB , BC , A B C is ...
... triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , measured on any broken line AB , BC , A B C is ...
Page 28
... triangle ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o . When G is A D without the triangle ABC . In the triangles GIC and AIB , we have , ( P. VII . ) , B4 ...
... triangle ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o . When G is A D without the triangle ABC . In the triangles GIC and AIB , we have , ( P. VII . ) , B4 ...
Page 29
... triangle ABC . From Proposition VIII . , we have , BA + BC > GA + GC ; or , since GA = BA , and GC = EF , B we have , BA + BC > BA + EF . Taking away the common part AB , there remains , BC > EF . A D E F Hence , in each case , BC is ...
... triangle ABC . From Proposition VIII . , we have , BA + BC > GA + GC ; or , since GA = BA , and GC = EF , B we have , BA + BC > BA + EF . Taking away the common part AB , there remains , BC > EF . A D E F Hence , in each case , BC is ...
Page 30
Adrien Marie Legendre. PROPOSITION X. THEOREM . If two triangles have the three sides of the one equal to the three sides of the other , each to each , the triangles will b equal in all their parts . In the triangles ABC and DEF , let AB ...
Adrien Marie Legendre. PROPOSITION X. THEOREM . If two triangles have the three sides of the one equal to the three sides of the other , each to each , the triangles will b equal in all their parts . In the triangles ABC and DEF , let AB ...
Page 31
... triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isos- celes . In the triangle ABC , let the angle ABC be equal to the angle ACB : then will AC be equal to AB , and consequently , the ...
... triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isos- celes . In the triangle ABC , let the angle ABC be equal to the angle ACB : then will AC be equal to AB , and consequently , the ...
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Common terms and phrases
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence