An Elementary Geometry |
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Page 5
... draw BE so that A B and B E shall form a straight line ; then ABD but by hypothesis , DBE two right angles ( 7 ) ; therefore ABD + DBC = two right angles ; DBE D B C the part equal to the whole , which is absurd ( Axiom 6 ) ; there ...
... draw BE so that A B and B E shall form a straight line ; then ABD but by hypothesis , DBE two right angles ( 7 ) ; therefore ABD + DBC = two right angles ; DBE D B C the part equal to the whole , which is absurd ( Axiom 6 ) ; there ...
Page 8
... drawn parallel to CD , it will make the opposite external and internal angles equal , and the alternate internal angles equal , and the internal angles on the same side equal ( 17 ) ; therefore it must coincide with AB ; that is , A B ...
... drawn parallel to CD , it will make the opposite external and internal angles equal , and the alternate internal angles equal , and the internal angles on the same side equal ( 17 ) ; therefore it must coincide with AB ; that is , A B ...
Page 10
... draw CD par- allel to A B ; then DCE A , be- A ing external internal angles ( 17 ) ; B D N С BCD B , being alternate internal angles ( 17 ) ; hence but - therefore DCE + BCD + BCA = A + B + B CA DCE BCD + BCA two right angles ( 7 ) ; A ...
... draw CD par- allel to A B ; then DCE A , be- A ing external internal angles ( 17 ) ; B D N С BCD B , being alternate internal angles ( 17 ) ; hence but - therefore DCE + BCD + BCA = A + B + B CA DCE BCD + BCA two right angles ( 7 ) ; A ...
Page 15
... drawn to this line , 1st . The perpendicular is shorter than any oblique line . 2d . Any two oblique lines equally distant from the perpendicu- lar are equal . 3d . Of two oblique lines the more remote is the greater . Let A be the ...
... drawn to this line , 1st . The perpendicular is shorter than any oblique line . 2d . Any two oblique lines equally distant from the perpendicu- lar are equal . 3d . Of two oblique lines the more remote is the greater . Let A be the ...
Page 16
... drawn , 1st . Any point in the perpendicular is equally distant from the extremities of the line . 2d . Any point ... draw DA and D B. Since C A C B , DA DB ( 51 ) . 2d . Let E be any point without the perpen- dicular ; draw E A and EB ...
... drawn , 1st . Any point in the perpendicular is equally distant from the extremities of the line . 2d . Any point ... draw DA and D B. Since C A C B , DA DB ( 51 ) . 2d . Let E be any point without the perpen- dicular ; draw E A and EB ...
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Common terms and phrases
A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube cylinder diagonals diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - 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 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 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.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.