An Elementary Geometry: Plane, Solid and Spherical1880 - 240 σελίδες |
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Σελίδα 8
... third are parallel to each other . 53. Definition . When parallel lines are cut by a third , the angles without the parallels are called external ; those within , internal ; thus , AGE , EG B , CHF , FHD are ex- ternal angles ; AGH ...
... third are parallel to each other . 53. Definition . When parallel lines are cut by a third , the angles without the parallels are called external ; those within , internal ; thus , AGE , EG B , CHF , FHD are ex- ternal angles ; AGH ...
Σελίδα 12
... third side D F is always considered the base . THEOREM IX . 73. The sum of the angles of a triangle is equal to two right angles . Let A B C be a triangle ; the sum of its three angles , A , B , C , is equal to two right angles ...
... third side D F is always considered the base . THEOREM IX . 73. The sum of the angles of a triangle is equal to two right angles . Let A B C be a triangle ; the sum of its three angles , A , B , C , is equal to two right angles ...
Σελίδα 13
... third of two right angles , or two thirds of one right angle . 79. Cor . 6. If any side of a triangle is produced , the exte- rior angle , as BCE , is equal to the sum of the two interior and opposite ; therefore it is greater than ...
... third of two right angles , or two thirds of one right angle . 79. Cor . 6. If any side of a triangle is produced , the exte- rior angle , as BCE , is equal to the sum of the two interior and opposite ; therefore it is greater than ...
Σελίδα 20
... third side of the one having the included angle greater is greater than the third side of the other . Let AB , BC , two sides of the triangle A B C , be respectively equal to AB , BD , two sides of the triangle A B D , but the angle ABC ...
... third side of the one having the included angle greater is greater than the third side of the other . Let AB , BC , two sides of the triangle A B C , be respectively equal to AB , BD , two sides of the triangle A B D , but the angle ABC ...
Σελίδα 21
... third sides unequal , the angle opposite this third side is greater in the triangle in which the third side is greater . Let AB , BC , two sides of the triangle AB C , be respectively equal to BD , BC of the triangle BD C , but A C > CD ...
... third sides unequal , the angle opposite this third side is greater in the triangle in which the third side is greater . Let AB , BC , two sides of the triangle AB C , be respectively equal to BD , BC of the triangle BD C , but A C > CD ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Geometry: Plane, Solid and Spherical William Frothingham Bradbury Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B D altitude angles are equal apothem arcs A B centre chord circle circumference circumscribed cone construct the triangle convex surface Corollary diagonals diameter diedral angles distance divided draw equally distant equivalent bases face angles feet frustum given angle given line given point hence homologous homologous lines hypothenuse inscribed intersection isosceles triangle lines bisecting locus medial line middle points mutually equiangular number of sides opposite sides parallelogram parallelopiped perimeter perpendicular plane M N polar triangle polyedral angle polyedrons produced proposition quadrilateral radius ratio rectangle rectangular parallelopiped regular polygon respectively equal right prism right triangle Scholium similar slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent tetraedrons THEOREM triangle A B C triangle is equal triangular prism triedral vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 166 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 13 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Σελίδα 41 - 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 198 - Each side of a spherical triangle is less than the sum of the other two sides.
Σελίδα 75 - 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.
Σελίδα 203 - In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB equal AC.
Σελίδα 220 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.
Σελίδα 136 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 199 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Σελίδα 162 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and GM.' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM'. Proof. The lateral edges of GM