## Elements of Geometry and Conic Sections |

### From inside the book

Page 15

... angles CBE , DBE be a

... angles CBE , DBE be a

**right angle**. Now the angle CBA is equal to the sum of the two angles CBE , EBA . each of ... (**Prop**. I. ) , and AB is perpendicular to DE . Cor . 3. The sum of all the angles BAC , CAD , DAE , EAF , formed on ... Page 16

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...

**right angles**(**Prop**. II . ) . But , by hypothesis , the angles ABC , ABD are together equal to two right angles ; therefore , the sum of the angles ABC , ABE is equal to the sum of the an- gles ABC , ABD . Take away the common angle ... Page 17

Elias Loomis. point E ; then will the angle AEC be equal to the angle BED , and the angle AED to the angle CEB ...

Elias Loomis. point E ; then will the angle AEC be equal to the angle BED , and the angle AED to the angle CEB ...

**right angles**(**Prop**. II . ) ; and the angles AED , DEB , which the straight line DE makes with the straight line AB ... Page 20

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...

**right angles**; and , conversely , the line bisecting the base of an isosceles triangle at**right angles**bisects also ...**Prop**. X. ) . If two angles of a triangle are equal to one another , the op- posite sides are also equel . Let ... Page 23

... (

... (

**Prop**. XIII . ) , which is also contrary to the hypothesis . Therefore , the**angle**A must be equal to the**angle**D ...**angles**are oppo- site to the equal sides ; thus , the equal**angles**A and D are opposite to the equal sides BC ...### Other editions - View all

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

### Common terms and phrases

75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment Sheep extra side AC similar 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 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.