Elements of Geometry: With Practical Applications to Mensuration |
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Page 5
... BOOK IV . PROPORTIONS , AREAS , AND SIMILARITY OF FIGURES 76 BOOK V. PROBLEMS RELATING TO THE PRECEDING BOOKS 118 BOOK VI . REGULAR POLYGONS , AND THE AREA OF THE CIRCLE · 149 SOLID GEOMETRY . BOOK VII . PLANES . DIEDRAL AND 1 *
... BOOK IV . PROPORTIONS , AREAS , AND SIMILARITY OF FIGURES 76 BOOK V. PROBLEMS RELATING TO THE PRECEDING BOOKS 118 BOOK VI . REGULAR POLYGONS , AND THE AREA OF THE CIRCLE · 149 SOLID GEOMETRY . BOOK VII . PLANES . DIEDRAL AND 1 *
Page 6
... FIGURES • BOOK XII . OF • • 253 APPLICATIONS OF GEOMETRY TO THE MENSURATION OF SOLIDS . · 281 BOOK XIII . MISCELLANEOUS GEOMETRICAL EXERCISES 801 BOOK XIV . APPLICATION OF ALGEBRA TO GEOMETRY 811 LELAND STANFORD JUNIOR UNIVER ELEMENTS ...
... FIGURES • BOOK XII . OF • • 253 APPLICATIONS OF GEOMETRY TO THE MENSURATION OF SOLIDS . · 281 BOOK XIII . MISCELLANEOUS GEOMETRICAL EXERCISES 801 BOOK XIV . APPLICATION OF ALGEBRA TO GEOMETRY 811 LELAND STANFORD JUNIOR UNIVER ELEMENTS ...
Page 10
... FIGURES . 19. A PLANE FIGURE is a plane terminated on all sides by straight lines or curves . The boundary of any figure is called its perimeter . 20. When the boundary lines are straight , the space they enclose is called a RECTILINEAL ...
... FIGURES . 19. A PLANE FIGURE is a plane terminated on all sides by straight lines or curves . The boundary of any figure is called its perimeter . 20. When the boundary lines are straight , the space they enclose is called a RECTILINEAL ...
Page 37
... figure has sides . Let ABCDE be any polygon ; then the sum of all its interior angles , A , B , C , D , E , is equal to twice as many right angles as the figure has sides , less four right angles . E D A B C For , from any point P ...
... figure has sides . Let ABCDE be any polygon ; then the sum of all its interior angles , A , B , C , D , E , is equal to twice as many right angles as the figure has sides , less four right angles . E D A B C For , from any point P ...
Page 38
... figure has sides , less four right angles . 103. Cor . 1. The sum of the angles in a quadrilateral is equal to four right angles ; hence , if all the angles of a quadrilateral are equal , each of them is a right angle ; also , if three ...
... figure has sides , less four right angles . 103. Cor . 1. The sum of the angles in a quadrilateral is equal to four right angles ; hence , if all the angles of a quadrilateral are equal , each of them is a right angle ; also , if three ...
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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.