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Elements of the Geometry of Planes and Solids: With Four Plates (Classic ...
F. R. Hassler
No preview available - 2018
ABCD altitude angle equal APPLIC base bisect called centre chord circle circumference common cone construction contain Corol cylinder Demonstr describe determine diagonal diameter difference distance divided double draw drawn equal equal angles equal base equal sides evidently expression fall figure four Geometry given given angle given point given triangle gives gles greater half included inscribed intersection inversely join less lies line BC meet obtained opposite parallel parallel planes parallelepiped parallelogram passing perpendicular plane poligon principles prisms PROBLEM Proof proportional protracted proved pyramid radii radius ratio rectilineal figure regular remains respectively resulting right angles Scholium segment sides similar smaller solid angles Solution sphere square straight line subtended Suppose supposition surface taken tangent thence THEOREM third side touch triangle ABC whole
Page 44 - In right angled triangles, the' rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Page 11 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 2 - BBOWN, of the said district, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : " Sertorius : or, the Roman Patriot.
Page 36 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 107 - If a solid angle be contained by three plane angles, any two of them are greater than the third.
Page 101 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.
Page 59 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and...
Page 29 - BFE; (i. def. 10.) therefore, in the two triangles, EAF, EBF, there are two angles in the one equal to two angles in the other, each to each; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (i.