## Elements of Geometry, Conic Sections, and Plane Trigonometry |

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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project No preview available - 2016 |

### Common terms and phrases

ABCD altitude angle ABC angle ACB base bisected called chord circle circumference coincide common cone consequently construct contained corresponding cosine curve described diagonals diameter difference distance divided draw drawn ellipse equal equivalent extremities fall figure formed four given greater half Hence hyperbola hypothenuse included inscribed intersect join less logarithm major axis manner mean measured meet multiplied opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION proved pyramid quadrant radius ratio reason rectangle regular remaining represent right angles Scholium secant segment side AC sides similar sine solid sphere spherical square straight line tangent THEOREM third triangle ABC vertex vertices VIII whole

### Popular passages

Page 20 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.

Page 148 - The radius of a sphere, is a straight line drawn from the center to any point of the surface.

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 34 - ... therefore the angle ACB is equal to the angle CBD. And because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel to BD.

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 159 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.

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.

Page 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 29 - If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also.

Page 151 - But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop.