Elements of Geometry: With Practical Applications to Mensuration |
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Page 7
... distance . The dimensions of extension are length , breadth , and height or thickness . 2. MAGNITUDE , in general , is that which has one or more of the three dimensions of extension . 3. A POINT is that which has position , without ...
... distance . The dimensions of extension are length , breadth , and height or thickness . 2. MAGNITUDE , in general , is that which has one or more of the three dimensions of extension . 3. A POINT is that which has position , without ...
Page 24
... distances from the perpendicular , will be equal . 3d . Of any two oblique lines , that which meets the given line at the greater distance from the perpendicular will be the longer . Let A be the given point , and DE the 24 ELEMENTS OF ...
... distances from the perpendicular , will be equal . 3d . Of any two oblique lines , that which meets the given line at the greater distance from the perpendicular will be the longer . Let A be the given point , and DE the 24 ELEMENTS OF ...
Page 25
... distances from the perpendicular , are equal . Thirdly . The point C being in the triangle ADF , the sum of the lines A C ... distance of any point from a straight line . 74. Cor . 2. From the same point to a given straight line only two ...
... distances from the perpendicular , are equal . Thirdly . The point C being in the triangle ADF , the sum of the lines A C ... distance of any point from a straight line . 74. Cor . 2. From the same point to a given straight line only two ...
Page 26
... distance from the perpendicular , and are therefore equal ( Prop . XIV . ) . So , likewise , the two oblique lines ... distances from the extremities A and B. 77. Cor . If a straight line have two points , of which each is equally ...
... distance from the perpendicular , and are therefore equal ( Prop . XIV . ) . So , likewise , the two oblique lines ... distances from the extremities A and B. 77. Cor . If a straight line have two points , of which each is equally ...
Page 35
... distance of the parallels AB , CD , at the point E , is equal to the side FH , which measures the distance of the same parallels at the point F. Hence two parallels are everywhere equally distant . PROPOSITION XXVI . — THEOREM . 92. If ...
... distance of the parallels AB , CD , at the point E , is equal to the side FH , which measures the distance of the same parallels at the point F. Hence two parallels are everywhere equally distant . PROPOSITION XXVI . — THEOREM . 92. If ...
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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.