An Elementary Geometry: Plane, Solid and Spherical1880 - 240 σελίδες |
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Σελίδα 2
... parts . 28. Magnitudes respectively equal to the same magnitude are equal to each other . 29. A straight line is the shortest distance between two points . PLANE GEOMETRY . BOOK I. POINTS , LINES , ANGLES 2 PLANE GEOMETRY .
... parts . 28. Magnitudes respectively equal to the same magnitude are equal to each other . 29. A straight line is the shortest distance between two points . PLANE GEOMETRY . BOOK I. POINTS , LINES , ANGLES 2 PLANE GEOMETRY .
Σελίδα 4
... All right angles are equal . D E Ꮐ B Let EF and GH be perpendicular respective- ly to the straight lines A B and C D ; the right A F B C D H angles A FE , CH G , E F B , G H D , are equal . Place the line A B on CD ; A B 4 PLANE GEOMETRY .
... All right angles are equal . D E Ꮐ B Let EF and GH be perpendicular respective- ly to the straight lines A B and C D ; the right A F B C D H angles A FE , CH G , E F B , G H D , are equal . Place the line A B on CD ; A B 4 PLANE GEOMETRY .
Σελίδα 5
... respectively bisected by the perpendiculars E F , GH , the angles A FE , CHG , EFB , G HD , must be equal ( 28 ) . 38. Scholium . In the measurement of angles , the right angle , being an invariable quantity , is often taken as unity ...
... respectively bisected by the perpendiculars E F , GH , the angles A FE , CHG , EFB , G HD , must be equal ( 28 ) . 38. Scholium . In the measurement of angles , the right angle , being an invariable quantity , is often taken as unity ...
Σελίδα 7
... respectively the same direc- tion as ED and EF , including the angle E ; then angle Bangle E. C A F For since BA has the same direction as ED , and BC the same as EF , the differ- ence of direction of BA and BC must be the same as the ...
... respectively the same direc- tion as ED and EF , including the angle E ; then angle Bangle E. C A F For since BA has the same direction as ED , and BC the same as EF , the differ- ence of direction of BA and BC must be the same as the ...
Σελίδα 8
... respectively opposite di- rections to E F and E D , including the angle E ; then angle Bangle E. Produce D E and FE so as to form the angle GEH ; then ( 48 ) and GEH DEF = B C D G E H F GEH ABC by the first part of this = proposition ...
... respectively opposite di- rections to E F and E D , including the angle E ; then angle Bangle E. Produce D E and FE so as to form the angle GEH ; then ( 48 ) and GEH DEF = B C D G E H F GEH ABC by the first part of this = proposition ...
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