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
... parallel lines • Of triangles Of quadrilaterals ... ... Additional Theorems of triangles ... parallels Construction of polygons Of contact • Of common measure ... ... THIRD BOOK . Definitions . Proportional lines Similar triangles ...
... parallel lines • Of triangles Of quadrilaterals ... ... Additional Theorems of triangles ... parallels Construction of polygons Of contact • Of common measure ... ... THIRD BOOK . Definitions . Proportional lines Similar triangles ...
Page 9
... Parallel lines are those which have the same direction . XI . An Angle is the difference in direction of two straight lines meeting or crossing each other . The Vertex of the angle is the point where its sides meet . XII . When one ...
... Parallel lines are those which have the same direction . XI . An Angle is the difference in direction of two straight lines meeting or crossing each other . The Vertex of the angle is the point where its sides meet . XII . When one ...
Page 11
... parallel , the figure is called a parallelogram . XXVI . When the four angles of a parallelo- gram are right angles , the figure is called a rectangle . XXVII . When the four sides of a rectangle are equal , the figure is called a ...
... parallel , the figure is called a parallelogram . XXVI . When the four angles of a parallelo- gram are right angles , the figure is called a rectangle . XXVII . When the four sides of a rectangle are equal , the figure is called a ...
Page 13
... parallel to another . XIII . Only one straight line can be drawn joining two given points . XIV . Straight lines which are parallel to the same line are parallel to each other . POSTULATES . I. Let it be granted that a straight line may ...
... parallel to another . XIII . Only one straight line can be drawn joining two given points . XIV . Straight lines which are parallel to the same line are parallel to each other . POSTULATES . I. Let it be granted that a straight line may ...
Page 15
... parallel are either equal or supplementary . First . When the sides AB and AC , forming the angle at A , have ... parallel , they have the same direction in reference to the line CG ( D. X. ) , consequently the angle BAC is equal ...
... parallel are either equal or supplementary . First . When the sides AB and AC , forming the angle at A , have ... parallel , they have the same direction in reference to the line CG ( D. X. ) , consequently the angle BAC is equal ...
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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.