An Elementary Geometry and TrigonometryThompson, Bigelow, and Brown, 1872 - 238 σελίδες |
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Αποτελέσματα 1 - 5 από τα 33.
Σελίδα 19
... half their sum . Let EF join the middle points of the sides A B and CD , which are not parallel , of the trapezoid ABCD ; then B E G C F 1st . EF is parallel to BC and AD . Through F draw GH parallel to B A , meeting AD produced in H ...
... half their sum . Let EF join the middle points of the sides A B and CD , which are not parallel , of the trapezoid ABCD ; then B E G C F 1st . EF is parallel to BC and AD . Through F draw GH parallel to B A , meeting AD produced in H ...
Σελίδα 33
... DF . THEOREM IV . 11. The area of a triangle is equal to half the product of its base and altitude . Let BD be the altitude of the triangle ABC ; then the area of ABC ACX BD . = C B E Draw CE parallel to AB , and BE 2 * BOOK II . 33.
... DF . THEOREM IV . 11. The area of a triangle is equal to half the product of its base and altitude . Let BD be the altitude of the triangle ABC ; then the area of ABC ACX BD . = C B E Draw CE parallel to AB , and BE 2 * BOOK II . 33.
Σελίδα 34
... half the parallelogram ABEC ( I. 63 ) ; the area of the parallelogram ACX BD ( 10 ) ; therefore the area of the triangle ACX BD . - A D 12. Cor . 1. Triangles are to each other as the products of their bases and altitudes . For if A and ...
... half the parallelogram ABEC ( I. 63 ) ; the area of the parallelogram ACX BD ( 10 ) ; therefore the area of the triangle ACX BD . - A D 12. Cor . 1. Triangles are to each other as the products of their bases and altitudes . For if A and ...
Σελίδα 43
... half the product of its perimeter and apothem . For the area of each triangle of which the polygon is com- posed is equal to half the product of its base and the apothem of the polygon ( 11 ) ; therefore the area of the polygon is equal ...
... half the product of its perimeter and apothem . For the area of each triangle of which the polygon is com- posed is equal to half the product of its base and the apothem of the polygon ( 11 ) ; therefore the area of the polygon is equal ...
Σελίδα 45
... half of the line . 40. The square on the difference AC of two straight lines A B , BC is equivalent to the squares on AB and BC , diminished by twice the rectangle AB . BC . Or , algebraically , if a = A B , and b ( a - b ) 2 = a2 — 2ab ...
... half of the line . 40. The square on the difference AC of two straight lines A B , BC is equivalent to the squares on AB and BC , diminished by twice the rectangle AB . BC . Or , algebraically , if a = A B , and b ( a - b ) 2 = a2 — 2ab ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B C ABCDEF acute angle adjacent altitude angle BCD apothem arc or angle bisect centre chord circumference comp cone construct the triangle convex surface Corollary cosec decr diagonals diameter distance divided draw equiangular equilateral equivalent feet Find the Log frustum Geom given angle given line given point given side hypothenuse included angle incr inscribed internal angles isosceles triangle lines A B Logarithm M.
M. Sine multiplied number of sides opposite side parallelogram parallelopiped perimeter perpendicular PLANE GEOMETRY plane triangle PLANE TRIGONOMETRY prism PROBLEM quadrilateral radii radius ratio rectangle regular polygon right angle right pyramid right triangle right-angled triangle Scholium secant segment side opposite similar triangles slant height sphere square straight line Tang tangent THEOREM THEOREM VII trapezoid triangle ABC TRIGONOMETRY vertex
Δημοφιλή αποσπάσματα
Σελίδα 30 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 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...
Σελίδα 49 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Σελίδα 96 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 12 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.
Σελίδα 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Σελίδα 71 - The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude.
Σελίδα 40 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Σελίδα 23 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.