Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Results 1-5 of 26
Page 28
... included angle of the one , equal to the two sides and the included angle of the other , the triangles will be identical , or equal in all respects . In the two triangles ABC , DFG , if the side CA be equal to the side DG , and the ...
... included angle of the one , equal to the two sides and the included angle of the other , the triangles will be identical , or equal in all respects . In the two triangles ABC , DFG , if the side CA be equal to the side DG , and the ...
Page 29
... angle ACG ( Post . VI . ) , and meet- B D E C F A L G D ing AB at L , draw GL . The two triangles ACL , GCL , are ... included angle of the first will be greater than the included angle of the second . For , if the included angle ...
... angle ACG ( Post . VI . ) , and meet- B D E C F A L G D ing AB at L , draw GL . The two triangles ACL , GCL , are ... included angle of the first will be greater than the included angle of the second . For , if the included angle ...
Page 31
... included angle ABD of the first triangle equal to BAC , the included angle of the second tri- angle . Hence ( T. XX . ) , the triangle BAD is equal to ABC , that is , a part is equal to the whole , which is impossible ( A. VIII ...
... included angle ABD of the first triangle equal to BAC , the included angle of the second tri- angle . Hence ( T. XX . ) , the triangle BAD is equal to ABC , that is , a part is equal to the whole , which is impossible ( A. VIII ...
Page 34
... included angles ABD , CDB , equal , being alternate angles with reference to the parallels AB , DC . Hence these triangles are equal ( T. XX . ) , and the angle ADB is equal to CBD , but these are alternate angles with reference to AD ...
... included angles ABD , CDB , equal , being alternate angles with reference to the parallels AB , DC . Hence these triangles are equal ( T. XX . ) , and the angle ADB is equal to CBD , but these are alternate angles with reference to AD ...
Page 35
... angle ADB = CBD . Therefore , the two triangles ABD and CDB have a common side BD , and the adjacent angles of the ... included between two other parallels are equal . Cor . III . If one angle of a parallelogram is right , the ...
... angle ADB = CBD . Therefore , the two triangles ABD and CDB have a common side BD , and the adjacent angles of the ... included between two other parallels are equal . Cor . III . If one angle of a parallelogram is right , the ...
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Common terms and phrases
ABCD altitude apothem base bisect centre chord circle circumference circumscribed column cone consequently corresponding cosec Cosine Cotang cube cubic cylinder decimal denote diameter dicular divided draw drawn equation EXAMPLES exterior angles feet figures formula frustum Geom gives greater half Hence hypotenuse inches included angle intersection logarithmic sine measure multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular polygon respectively equal right angles right triangles right-angled triangle Scholium secant sector similar similar triangles sine slant height solid solve the triangle sphere spherical triangle square straight line subtract suppose surface tang tangent THEOREM three sides triangle ABC triangular prism volume
Popular passages
Page 35 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 80 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 17 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Page 176 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 182 - Every section of a sphere, made by a plane, is a circle.
Page 28 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B
Page 165 - ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes.
Page 29 - ... to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is.
Page 13 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.