Essentials of GeometryS.C. Griggs, 1883 - 267 σελίδες |
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Σελίδα 9
... intersect , each other , four angles are formed about the point of intersection , which are distin- guished as follows : 1. Those which lie on the same side of one of the lines and on opposite sides of the other are called Adjacent ...
... intersect , each other , four angles are formed about the point of intersection , which are distin- guished as follows : 1. Those which lie on the same side of one of the lines and on opposite sides of the other are called Adjacent ...
Σελίδα 10
... intersect , the vertical angles will be equal . D Let the two lines A B and CD intersect at O ; For , Also , C a Xb d then and B a + c = 2R- b + c = 2 R a + c = b + c a = b a + d = 2R- · Again , Also , a + c = 2 R ... a + c = a + d c ...
... intersect , the vertical angles will be equal . D Let the two lines A B and CD intersect at O ; For , Also , C a Xb d then and B a + c = 2R- b + c = 2 R a + c = b + c a = b a + d = 2R- · Again , Also , a + c = 2 R ... a + c = a + d c ...
Σελίδα 12
... intersect ? ( See Ax . 7. ) Three lines ? 7. If five of six angles formed in a plane about a point are 12 ° , 30 ° , 48 ° , 75 ° and 148 ° , how many degrees are there in the sixth angle ? r DEFINITIONS . 1. A Plane Surface , or simply ...
... intersect ? ( See Ax . 7. ) Three lines ? 7. If five of six angles formed in a plane about a point are 12 ° , 30 ° , 48 ° , 75 ° and 148 ° , how many degrees are there in the sixth angle ? r DEFINITIONS . 1. A Plane Surface , or simply ...
Σελίδα 24
... intersect two parallel lines in order that all the angles may be equal ? THEOREM IX . If a straight line cut two other straight lines , making the sum of the interior angles on the same side equal to two right angles , the two lines cut ...
... intersect two parallel lines in order that all the angles may be equal ? THEOREM IX . If a straight line cut two other straight lines , making the sum of the interior angles on the same side equal to two right angles , the two lines cut ...
Σελίδα 64
... intersect in only two points . For , if they intersect in a third , they will coincide . THEOREM X. A straight line can intersect a circumference in only two points . A D F B E Let C be a circle , and AB a straight line ; then can A B ...
... intersect in only two points . For , if they intersect in a third , they will coincide . THEOREM X. A straight line can intersect a circumference in only two points . A D F B E Let C be a circle , and AB a straight line ; then can A B ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B and C D ABCD adjacent angles angle equal apothem bisect central angles centre circle whose radius circumference coincide construct convex surface cylinder diagonals diameter distance divided draw drawn equal altitudes equal bases equal circles equally distant equiangular EXERCISES feet frustum generatrix given angle given circle given line given point greater Hence homologous sides hypotenuse included angle inscribed angle inscribed circle interior angles intersect isosceles triangle lune number of sides oblique parallel parallelogram parallelopiped perimeter perpendicular plane prism Prob proportional pyramid Q. E. D. Cor Q. E. F quadrilateral QUERIES radii ratio rectangle regular polygon right cone right triangle Scholium secant segments similar slant height sphere spherical triangle square straight line tangent triangle A B C vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 18 - if two triangles have two sides of the one equal to two sides of the...
Σελίδα 110 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon it.
Σελίδα 13 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Σελίδα 107 - 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, they are equal in all their parts.
Σελίδα 24 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 38 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Σελίδα 42 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Σελίδα 232 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 14 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα x - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.