Elements of Geometry: With Practical Applications to Mensuration |
From inside the book
Results 1-5 of 86
Page 25
... half of ABF , is shorter than A C , the half of ACF ; hence the perpendicular is shorter than any oblique line . Secondly . If BE is equal to B C , then , since A B is common to the triangles , A B E , ABC , and the angles ABE , ABC are ...
... half of ABF , is shorter than A C , the half of ACF ; hence the perpendicular is shorter than any oblique line . Secondly . If BE is equal to B C , then , since A B is common to the triangles , A B E , ABC , and the angles ABE , ABC are ...
Page 63
... half of A B , is equal to the side D G , the half of DE ; therefore the triangles are equal , and CF is equal to CG ( Prop . XIX . Bk . I. ) ; hence the two equal chords A B , D E are equally distant from the center . Conversely , if ...
... half of A B , is equal to the side D G , the half of DE ; therefore the triangles are equal , and CF is equal to CG ( Prop . XIX . Bk . I. ) ; hence the two equal chords A B , D E are equally distant from the center . Conversely , if ...
Page 72
... half of the arc BD . First . Suppose the center of the circle C to lie within the angle BAD . Draw the diameter A E ... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC and CAD together , or ...
... half of the arc BD . First . Suppose the center of the circle C to lie within the angle BAD . Draw the diameter A E ... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC and CAD together , or ...
Page 73
... half of the same arc , BOC . 202. Cor . 2. Every angle , BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circumference , BOD ; B that is , by the fourth part of the whole circumference ...
... half of the same arc , BOC . 202. Cor . 2. Every angle , BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circumference , BOD ; B that is , by the fourth part of the whole circumference ...
Page 74
... half the arc FDB ( Prop . XVIII . ) ; that is , by half the arc D B , plus half the arc FD . Hence , since FD is equal to A C , the angle DEB , or its equal angle A EC , is measured by half the sum of the intercepted arcs DB and AC ...
... half the arc FDB ( Prop . XVIII . ) ; that is , by half the arc D B , plus half the arc FD . Hence , since FD is equal to A C , the angle DEB , or its equal angle A EC , is measured by half the sum of the intercepted arcs DB and AC ...
Other editions - View all
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.