Elements of Geometry and Conic Sections |
From inside the book
Results 1-5 of 30
Page 12
... . 9. The whole is greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. From one point to another only one straight line can be drawn . 12. Two straight lines , which intersect one another , 12 GEOMETRY .
... . 9. The whole is greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. From one point to another only one straight line can be drawn . 12. Two straight lines , which intersect one another , 12 GEOMETRY .
Page 13
Elias Loomis. 12. Two straight lines , which intersect one another , can not both be parallel to the same straight line . Explanation of Signs . For the sake of brevity , it is convenient to employ , to some extent , the signs of Algebra ...
Elias Loomis. 12. Two straight lines , which intersect one another , can not both be parallel to the same straight line . Explanation of Signs . For the sake of brevity , it is convenient to employ , to some extent , the signs of Algebra ...
Page 17
... intersection , are together equal to four right angles . Cor . 2. Hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . X PROPOSITION VI . THEOREM . If two triangles ...
... intersection , are together equal to four right angles . Cor . 2. Hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . X PROPOSITION VI . THEOREM . If two triangles ...
Page 18
... intersection , D. Hence the two triangles ABC , DEF coincide throughout , and are equal to each other ; also , the two sides AB , AC are equal to the two sides DE , DF , each to each , and the angle A to the angle D. Therefore , if two ...
... intersection , D. Hence the two triangles ABC , DEF coincide throughout , and are equal to each other ; also , the two sides AB , AC are equal to the two sides DE , DF , each to each , and the angle A to the angle D. Therefore , if two ...
Page 28
... intersect two parallel lines , it makes the alternate angles equal to each other ; also , any exterior angle equal to the interior and opposite on the same side ; and the two interior angles on the same side together equal to two right ...
... intersect two parallel lines , it makes the alternate angles equal to each other ; also , any exterior angle equal to the interior and opposite on the same side ; and the two interior angles on the same side together equal to two right ...
Common terms and phrases
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Popular passages
Page 17 - 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, the two triangles will be equal.
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 30 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.