Elements of Geometry: With Practical Applications to Mensuration |
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Page 11
... ISOSCELES TRIANGLE is one which has two of its sides equal ; as the triangle DEF . A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle G H I. 23. A RIGHT - ANGLED TRIANGLE is one which has a right angle ; as ...
... ISOSCELES TRIANGLE is one which has two of its sides equal ; as the triangle DEF . A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle G H I. 23. A RIGHT - ANGLED TRIANGLE is one which has a right angle ; as ...
Page 12
... isosceles triangle , it is usual to consider that side the base which is not equal to either of the other sides . 31. An equilateral polygon is one which has all its sides equal . An equiangular polygon is one which has all its angles ...
... isosceles triangle , it is usual to consider that side the base which is not equal to either of the other sides . 31. An equilateral polygon is one which has all its sides equal . An equiangular polygon is one which has all its angles ...
Page 19
... isosceles triangle , the angles opposite the equal sides are equal . Let ABC be an isosceles triangle , in which the side AB is equal to the side AC ; then will the angle B be equal to the angle C. Conceive the angle B A C to be bisect ...
... isosceles triangle , the angles opposite the equal sides are equal . Let ABC be an isosceles triangle , in which the side AB is equal to the side AC ; then will the angle B be equal to the angle C. Conceive the angle B A C to be bisect ...
Page 20
... isosceles triangle bisects the base at right angles . 58. Cor . 2. Conversely , the line bisecting the base of an isosceles triangle at right angles , bisects also the verti- cal angle . 59. Cor . 3. Every equilateral triangle is also ...
... isosceles triangle bisects the base at right angles . 58. Cor . 2. Conversely , the line bisecting the base of an isosceles triangle at right angles , bisects also the verti- cal angle . 59. Cor . 3. Every equilateral triangle is also ...
Page 61
... isosceles ; and the line CE bisects the base A B at right angles ; therefore CE bisects also the angle ACB ( Prop . VII . Cor . 2 , Bk . I. ) . Since the an- gles A CD , D C B are equal , the arcs A E , EB are equal ( Prop . V ...
... isosceles ; and the line CE bisects the base A B at right angles ; therefore CE bisects also the angle ACB ( Prop . VII . Cor . 2 , Bk . I. ) . Since the an- gles A CD , D C B are equal , the arcs A E , EB are equal ( Prop . V ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B 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 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 polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon 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.