Elements of Geometry and Conic Sections |
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Page 23
... drawn to that line . Let A be the given point , and DE the given straight line ; from the point A only one perpendicular can be drawn to DE . A CB D E For , if possible , let there be drawn two perpendiculars AB , AC . Produce the line ...
... drawn to that line . Let A be the given point , and DE the given straight line ; from the point A only one perpendicular can be drawn to DE . A CB D E For , if possible , let there be drawn two perpendiculars AB , AC . Produce the line ...
Page 24
... drawn to this line , and oblique lines be drawn to different points : 1st . The perpendicular will be shorter than ... draw , also , the ob- lique lines AC , AD , AE . line AB to F , making BF and join CF , DF . Produce the equal to AB ...
... drawn to this line , and oblique lines be drawn to different points : 1st . The perpendicular will be shorter than ... draw , also , the ob- lique lines AC , AD , AE . line AB to F , making BF and join CF , DF . Produce the equal to AB ...
Page 25
... draw three equal straight lines from the same point to a given straight line . PROPOSITION XVIII . THEOREM . If through the middle point of a straight line a perpendic- ular is drawn to this line : 1st . Each point in the perpendicular ...
... draw three equal straight lines from the same point to a given straight line . PROPOSITION XVIII . THEOREM . If through the middle point of a straight line a perpendic- ular is drawn to this line : 1st . Each point in the perpendicular ...
Page 29
... draw any straight line , as C PQR , perpendicular to EF . Then , since AB is parallel to EF , PR , which A- is perpendicular to EF , will also be R Q -D -B perpendicular to AB ( Prop . XXIII . , Cor . 1 ) ; and since CD is parallel to ...
... draw any straight line , as C PQR , perpendicular to EF . Then , since AB is parallel to EF , PR , which A- is perpendicular to EF , will also be R Q -D -B perpendicular to AB ( Prop . XXIII . , Cor . 1 ) ; and since CD is parallel to ...
Page 31
... drawn parallel to the side AB of the triangle ; then , because AB is parallel to CE , and AC meets them , the alternate ... draw lines FA , FB , FC , & c , to all the angles . The polygon is thus divided into as many tri ingles as it has ...
... drawn parallel to the side AB of the triangle ; then , because AB is parallel to CE , and AC meets them , the alternate ... draw lines FA , FB , FC , & c , to all the angles . The polygon is thus divided into as many tri ingles as it has ...
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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 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
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
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, their third sides will be equal, and their other angles will be equal, each to each.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
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 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 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 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
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 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.