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 77
... multiply a surface by a line , a surface by a surface , and even a volume by a volume , etc. But in all these cases it must be ... multiplied . SIMILAR TRIANGLES . THEOREM IV . A straight line drawn parallel to either side of a triangle ...
... multiply a surface by a line , a surface by a surface , and even a volume by a volume , etc. But in all these cases it must be ... multiplied . SIMILAR TRIANGLES . THEOREM IV . A straight line drawn parallel to either side of a triangle ...
Page 90
... XXI . Any two rectangles are to each other as the product of their bases multiplied by their altitudes . Let ABCD , AFGH be two rectangles , then will ABCD : AFGH :: AB × AD : AH × AF . F K G A H C B A Having placed 90 GEOMETRY .
... XXI . Any two rectangles are to each other as the product of their bases multiplied by their altitudes . Let ABCD , AFGH be two rectangles , then will ABCD : AFGH :: AB × AD : AH × AF . F K G A H C B A Having placed 90 GEOMETRY .
Page 91
... Multiplying the corresponding terms of these proportions together , and observing to omit AFKD , since it will occur in an antecedent and consequent , we shall have ABCD : AFGH :: ABXAD : AHXAF . Scholium . Hence we are at liberty to ...
... Multiplying the corresponding terms of these proportions together , and observing to omit AFKD , since it will occur in an antecedent and consequent , we shall have ABCD : AFGH :: ABXAD : AHXAF . Scholium . Hence we are at liberty to ...
Page 92
... multiplied by itself . The squares of the numbers 1 , 2 , 3 , etc. , are 1 , 4 , 9 , etc. From which we see that the square formed on a line of double length is quadruple ; on a line of triple length it is nine times as great , and so ...
... multiplied by itself . The squares of the numbers 1 , 2 , 3 , etc. , are 1 , 4 , 9 , etc. From which we see that the square formed on a line of double length is quadruple ; on a line of triple length it is nine times as great , and so ...
Page 95
... Multiplying together the corresponding terms of these pro- portions , and omitting the common term ADC which enters into the antecedent and consequent of the first couplet , we have ABC : ADE :: AB × AC : AD × AE . Cor . Whenever the ...
... Multiplying together the corresponding terms of these pro- portions , and omitting the common term ADC which enters into the antecedent and consequent of the first couplet , we have ABC : ADE :: AB × AC : AD × AE . Cor . Whenever the ...
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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.