Elements of Geometry and Conic SectionsHarper, 1858 - 234 Seiten |
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Seite 5
... contain , indeed , the essential part of an argument ; but the general student does not derive from them the high est benefit which may accrue from the study of Geometry as an exercise in reasoning . While , then , in the following ...
... contain , indeed , the essential part of an argument ; but the general student does not derive from them the high est benefit which may accrue from the study of Geometry as an exercise in reasoning . While , then , in the following ...
Seite 10
... contained by the straight lines BC , CD , is called the angle BCD , or DCB . B E D Angles , like other quantities , may be added , subtracted , multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and ...
... contained by the straight lines BC , CD , is called the angle BCD , or DCB . B E D Angles , like other quantities , may be added , subtracted , multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and ...
Seite 10
... contained by the straight lines BC , CD , is called the angle BCD , or DCB . B E D Angles , like other quantities , may be added , subtracted , multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and ...
... contained by the straight lines BC , CD , is called the angle BCD , or DCB . B E D Angles , like other quantities , may be added , subtracted , multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and ...
Seite 22
... contained by the sides of the other . Let ABC , DEF be two triangles having two sides of the one equal to A two sides of the other , viz .: AB equal to DE , and AC to DF , but the base BC greater than the base EF ; then will the angle ...
... contained by the sides of the other . Let ABC , DEF be two triangles having two sides of the one equal to A two sides of the other , viz .: AB equal to DE , and AC to DF , but the base BC greater than the base EF ; then will the angle ...
Seite 30
... contain the angles are similarly situ- ated ; because , if we produce FE to H , the angle DEH has its sides parallel to those of the angle BAC ; but the two an- gles are not equal . PROPOSITION XXVII . THEOREM . If one side of a ...
... contain the angles are similarly situ- ated ; because , if we produce FE to H , the angle DEH has its sides parallel to those of the angle BAC ; but the two an- gles are not equal . PROPOSITION XXVII . THEOREM . If one side of a ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Seite 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.
Seite 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.