An Elementary Geometry: Plane, Solid and Spherical1880 - 240 σελίδες |
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Σελίδα 1
... formed of different straight lines ; as ABCDE . B D A E C 9. A Curved Line is one whose direction D is constantly changing ; as CD . 10. A Surface has length and breadth , but no thickness . 1 11. A Plane is such a surface that a ...
... formed of different straight lines ; as ABCDE . B D A E C 9. A Curved Line is one whose direction D is constantly changing ; as CD . 10. A Surface has length and breadth , but no thickness . 1 11. A Plane is such a surface that a ...
Σελίδα 5
... formed at F by FA and FB is equal to the angle formed at H by HC and HD ; and as these equal angles are respectively bisected by the perpendiculars E F , GH , the angles A FE , CHG , EFB , G HD , must be equal ( 28 ) . 38. Scholium . In ...
... formed at F by FA and FB is equal to the angle formed at H by HC and HD ; and as these equal angles are respectively bisected by the perpendiculars E F , GH , the angles A FE , CHG , EFB , G HD , must be equal ( 28 ) . 38. Scholium . In ...
Σελίδα 6
... formed , D each is the supplement of the other . For by the theorem , ACD + DCB = two angles ; therefore AC D = two right angles - DCB , or DC B two right angles - A CD . A B 46. Cor . 2. The sum of all the angles formed in a plane ...
... formed , D each is the supplement of the other . For by the theorem , ACD + DCB = two angles ; therefore AC D = two right angles - DCB , or DC B two right angles - A CD . A B 46. Cor . 2. The sum of all the angles formed in a plane ...
Σελίδα 9
... parallel lines , the four acute angles formed are equal ; and also the four obtuse angles ; and of these angles any acute angle and obtuse angle are supplements of each other . THEOREM VII . CONVERSE OF THEOREM VI . 56. If BOOK I.
... parallel lines , the four acute angles formed are equal ; and also the four obtuse angles ; and of these angles any acute angle and obtuse angle are supplements of each other . THEOREM VII . CONVERSE OF THEOREM VI . 56. If BOOK I.
Σελίδα 30
... formed at a point on the same side of a straight line , in the same plane , contain respectively 15 ° , 27 ° , and 99 ° , how many degrees does the fourth angle contain ? 5. If five of six angles formed in a plane about a point are ...
... formed at a point on the same side of a straight line , in the same plane , contain respectively 15 ° , 27 ° , and 99 ° , how many degrees does the fourth angle contain ? 5. If five of six angles formed in a plane about a point are ...
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