Elements of Geometry: With Practical Applications to Mensuration |
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Page 9
... formed by a straight line and a perpendicular to it ; as the angle CAB . 16. An ACUTE ANGLE is one which is less than a right angle ; as the angle DEF . C -B A D E F E An OBTUSE ANGLE is one which is greater than a right angle ; as the ...
... formed by a straight line and a perpendicular to it ; as the angle CAB . 16. An ACUTE ANGLE is one which is less than a right angle ; as the angle DEF . C -B A D E F E An OBTUSE ANGLE is one which is greater than a right angle ; as the ...
Page 15
... formed on the same side of a straight line , BF , are equal , when taken together , to two right angles ; for their sum is equal to that of the two adjacent angles , BAC , CAF . D E B F A PROPOSITION II . - THEOREM . 47. If one straight ...
... formed on the same side of a straight line , BF , are equal , when taken together , to two right angles ; for their sum is equal to that of the two adjacent angles , BAC , CAF . D E B F A PROPOSITION II . - THEOREM . 47. If one straight ...
Page 17
... CEB is equal to its opposite angle , A ED . 50. Cor . 1. The four angles formed by two straight lines intersecting each other , are together equal to four right angles . 51. Cor . 2. All the successive angles , around 2 * BOOK I. 17.
... CEB is equal to its opposite angle , A ED . 50. Cor . 1. The four angles formed by two straight lines intersecting each other , are together equal to four right angles . 51. Cor . 2. All the successive angles , around 2 * BOOK I. 17.
Page 18
... formed by any number of straight lines meet- ing at that point , are together equal to four right angles . PROPOSITION V. — THEOREM . 52. If two triangles have two sides and the included angle in the one equal to two sides and the ...
... formed by any number of straight lines meet- ing at that point , are together equal to four right angles . PROPOSITION V. — THEOREM . 52. If two triangles have two sides and the included angle in the one equal to two sides and the ...
Page 30
... HI . Then the opposite angles KOG , IOH , formed by the intersection of the two straight lines IK , GH , are equal ( Prop . IV . ) ; and the triangles KOG , IOH have the two sides KO , OG and the 30 ELEMENTS OF GEOMETRY .
... HI . Then the opposite angles KOG , IOH , formed by the intersection of the two straight lines IK , GH , are equal ( Prop . IV . ) ; and the triangles KOG , IOH have the two sides KO , OG and the 30 ELEMENTS OF GEOMETRY .
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Common terms and phrases
A B C ABCD adjacent angles altitude angle equal base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed formulæ frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon Required the area right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - 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 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.