## Elements of Geometry and Conic Sections |

### Inni boken

Resultat 1-5 av 17

Side 6

Some acquaintance with the properties of the

indispensable as a preparation for the study of Mechanics and Astronomy .

Those who pursue the study of Analytical Geometry can omit this treatise on the

Conic Sections if ...

Some acquaintance with the properties of the

**Ellipse**and Parabola isindispensable as a preparation for the study of Mechanics and Astronomy .

Those who pursue the study of Analytical Geometry can omit this treatise on the

Conic Sections if ...

Side 7

Proposition in the same Book , only the number of the Proposition is given ; but

when the Proposition is found in a different Book , the number of the Book is also

specified ...

**Ellipse**Hyperbola 177 . 188 . • 205 N.B. — When reference is made to aProposition in the same Book , only the number of the Proposition is given ; but

when the Proposition is found in a different Book , the number of the Book is also

specified ...

Side 177

These are The Parabola , The

Definitions . 1. A parabola is a plane curve , every point of which is equally distant

from a fixed point , and a given straight line . 2. The fixed point is called the focus

of ...

These are The Parabola , The

**Ellipse**, and The Hyperbola . PARABOL A. Α ,Definitions . 1. A parabola is a plane curve , every point of which is equally distant

from a fixed point , and a given straight line . 2. The fixed point is called the focus

of ...

Side 187

... the whole space AVG is double the space ABV . Whence AVG is two thirds of

ABVG ; and the segment AVD is two thirds of the rectan- gle ABCD . Therefore ,

every segment , & c . !

... the whole space AVG is double the space ABV . Whence AVG is two thirds of

ABVG ; and the segment AVD is two thirds of the rectan- gle ABCD . Therefore ,

every segment , & c . !

**ELLIPSE**. X Definitions . B 1. An**ellipse**PARABOLA . 187. Side 188

distances of each point from two fixed points , is equal to a given line . 2. The two

fixed points are called the foci . Thus , if F , F are two fixed points , and if the ...

**ELLIPSE**. X Definitions . B 1. An**ellipse**is a plane curve , in which the sum of thedistances of each point from two fixed points , is equal to a given line . 2. The two

fixed points are called the foci . Thus , if F , F are two fixed points , and if the ...

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

### Populære avsnitt

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

Side 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.

Side 101 - When you have proved that the three angles of every triangle are equal to two right angles...

Side 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.

Side 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.

Side 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.

Side 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.

Side 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.

Side 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.

Side 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.