## Elements of Geometry and Conic Sections |

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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 angle BAC base bisected called cents chord circle circumference coincide common cone consequently construct contained convex surface curve described diameter difference distance divided draw drawn ellipse equal equal to AC equivalent faces fall figure foci focus formed four frustum given greater half hence hyperbola included inscribed intersection join less major axis manner mean measured meet Muslin opposite parallel parallelogram parallelopiped pass perpendicular plane plane MN polygon prism Prop proportional PROPOSITION proved pyramid radii radius ratio reason rectangle regular represent right angles Scholium segment Sheep extra sides similar solid sphere spherical square straight line tangent THEOREM third triangle ABC vertex vertices VIII whole

### Popular passages

Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 27 - VIf 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...

Page 11 - A rhombus, is that which has all its sides equal, but its angles are not 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 15 - 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 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.

Page 148 - I.), that every section of a sphere made by a plane is a circle.