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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Page v
... Construction of polygons .. Of contact Of common measure 42 47 51 • 57 61 • 66 69 70 Definitions . Proportional lines Similar triangles • THIRD BOOK . 73 74 1717 Similar polygons Proportional lines -- properties of the sides of.
... Construction of polygons .. Of contact Of common measure 42 47 51 • 57 61 • 66 69 70 Definitions . Proportional lines Similar triangles • THIRD BOOK . 73 74 1717 Similar polygons Proportional lines -- properties of the sides of.
Page 16
... third angle , which will be equal to the second . But this third angle is either equal to the first or supplementary to it ( T. II . ) . Consequently the second angle is either equal to the first or supplementary to it ( A. I. ) ...
... third angle , which will be equal to the second . But this third angle is either equal to the first or supplementary to it ( T. II . ) . Consequently the second angle is either equal to the first or supplementary to it ( A. I. ) ...
Page 17
... two triangles have two angles of the one respec- tively equal to two angles of the other , their third angles will be equal , and the triangles will be mutually equiangular . Cor . IV . In any quadrilateral , the sum 2 FIRST BOOK . 17.
... two triangles have two angles of the one respec- tively equal to two angles of the other , their third angles will be equal , and the triangles will be mutually equiangular . Cor . IV . In any quadrilateral , the sum 2 FIRST BOOK . 17.
Page 25
... third line , the angles formed receive particular names . WHEN TAKEN SEPARATELY : G B A H C D F 1. The four angles AGF , CHE , BGF , and DHE , situated within the parallels , are called interior angles . 2. The four angles AGE , CHF ...
... third line , the angles formed receive particular names . WHEN TAKEN SEPARATELY : G B A H C D F 1. The four angles AGF , CHE , BGF , and DHE , situated within the parallels , are called interior angles . 2. The four angles AGE , CHF ...
Page 26
... third line , they will be parallel : I. When the sum of the exterior angles on the same side is equal to two right angles . II . When the alternate interior angles are equal . III . When the alternate exterior angles are equal . IV ...
... third line , they will be parallel : I. When the sum of the exterior angles on the same side is equal to two right angles . II . When the alternate interior angles are equal . III . When the alternate exterior angles are equal . IV ...
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Common terms and phrases
a+b+c altitude apothem bisect centre chord circumference circumscribed cone consequently corresponding cosec Cosine Cotang cube cubic cylinder decimal denote diameter dicular divided draw drawn equation equivalent exterior angles feet figure frustum Geom give greater half hence hypotenuse inches intersection logarithm 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 inscribed regular polygon respectively equal right angles 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 ΙΟ
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.