An Elementary Geometry: Plane, Solid and Spherical1880 - 240 σελίδες |
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Σελίδα 6
... angles ( 44 ) ; therefore the sum of all the angles at the point B is equal to four right angles . THEOREM III . 47. If at a point in a straight line two other straight lines upon opposite sides of it make the sum of the adjacent angles ...
... angles ( 44 ) ; therefore the sum of all the angles at the point B is equal to four right angles . THEOREM III . 47. If at a point in a straight line two other straight lines upon opposite sides of it make the sum of the adjacent angles ...
Σελίδα 7
... angles whose sides have the same or opposite directions are equal . 1st . Let BA and B C , including the angle B , have respectively the same direc- tion as ED and EF , including the angle E ; then angle Bangle E. C A F For since BA has ...
... angles whose sides have the same or opposite directions are equal . 1st . Let BA and B C , including the angle B , have respectively the same direc- tion as ED and EF , including the angle E ; then angle Bangle E. C A F For since BA has ...
Σελίδα 8
... opposite di- rections to E F and E D , including the angle E ; then angle ... angles without the parallels are called external ; those within , internal ; thus ... sides of the secant , and not adjacent , are called alternate internal ...
... opposite di- rections to E F and E D , including the angle E ; then angle ... angles without the parallels are called external ; those within , internal ; thus ... sides of the secant , and not adjacent , are called alternate internal ...
Σελίδα 9
... opposite external and in- ternal angles ; as EGA and GHC , or E G B and G H D. THEOREM VI . 54. If a straight line ... sides have respectively the same directions ( 49 ) . E G A H D F 2d . The alternate internal angles , A G H and GHD , or ...
... opposite external and in- ternal angles ; as EGA and GHC , or E G B and G H D. THEOREM VI . 54. If a straight line ... sides have respectively the same directions ( 49 ) . E G A H D F 2d . The alternate internal angles , A G H and GHD , or ...
Σελίδα 10
... opposite external and internal angles equal , and the alternate internal angles equal , and the internal angles on the same side supplements of each other ( 54 ) ; therefore it must coincide with AB ; that is , AB is parallel to CD ...
... opposite external and internal angles equal , and the alternate internal angles equal , and the internal angles on the same side supplements of each other ( 54 ) ; therefore it must coincide with AB ; that is , AB is parallel to 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