Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Σελίδα 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 .
Σελίδα 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 ...
Σελίδα 27
... intersects two parallel lines , the in- terior angles on the same side , are those which lie within the parallels , A- and on the same side of the secant ine , as AGH , GHC ; also , BGH , GHD . Alternate angles lie within the parallels ...
... intersects two parallel lines , the in- terior angles on the same side , are those which lie within the parallels , A- and on the same side of the secant ine , as AGH , GHC ; also , BGH , GHD . Alternate angles lie within the parallels ...
Σελίδα 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 ...
Σελίδα 34
... intersect each other in E ; then will AE be equal to ED , and BE to EC . A C B Because the alternate angles ABE , ECD are equal ( Prop . XXIII . ) , and also the alternate angles EAB , EDC , the triangles ABE , DCE have two angles in ...
... intersect each other in E ; then will AE be equal to ED , and BE to EC . A C B Because the alternate angles ABE , ECD are equal ( Prop . XXIII . ) , and also the alternate angles EAB , EDC , the triangles ABE , DCE have two angles in ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 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, their third sides will be equal, and their other angles will be equal, each to each.
Σελίδα 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Σελίδα 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.
Σελίδα 44 - 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.