## Plane and Solid Geometry |

### From inside the book

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Page 76

A polygon is

circle is then said to be circumscribed about the polygon . PROPOSITION II .

THEOREM 177 . In the same circle , or equal circles , equal arcs are subtended

by ...

A polygon is

**inscribed**in a circle , if all its vertices are in the circumference . Thecircle is then said to be circumscribed about the polygon . PROPOSITION II .

THEOREM 177 . In the same circle , or equal circles , equal arcs are subtended

by ...

Page 77

The diagonals of an equilateral pentagon

310 . The radii drawn to the vertices of an

the figure into six equilateral triangles . Ex . 311 . If two chords bisect each other ...

The diagonals of an equilateral pentagon

**inscribed**in a circle are equal . B Ex .310 . The radii drawn to the vertices of an

**inscribed**equilateral hexagon dividethe figure into six equilateral triangles . Ex . 311 . If two chords bisect each other ...

Page 78

If the perpendiculars from the center upon the sides of an

equal , the polygon is equilateral . Ex . 315 . If from a point without a circle two

equal lines are drawn to a circumference , the bisector of the angle they form

passes ...

If the perpendiculars from the center upon the sides of an

**inscribed**polygon areequal , the polygon is equilateral . Ex . 315 . If from a point without a circle two

equal lines are drawn to a circumference , the bisector of the angle they form

passes ...

Page 84

The side of an equilateral hexagon

than the side of an equilateral heptagon

remote from the center than the side of an equi . lateral pentagon

...

The side of an equilateral hexagon

**inscribed**in a circle is nearer to the centerthan the side of an equilateral heptagon

**inscribed**in the same circle , and moreremote from the center than the side of an equi . lateral pentagon

**inscribed**in the...

Page 93

The numerical measure of any central angle is equal to the numerical measure of

the intercepted arc , or more briefly : 216 . A central angle is measured by the

intercepted arc , DEFINITIONS 217 . An

The numerical measure of any central angle is equal to the numerical measure of

the intercepted arc , or more briefly : 216 . A central angle is measured by the

intercepted arc , DEFINITIONS 217 . An

**inscribed**angle of a circle is LIMITS.### What people are saying - Write a review

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### Common terms and phrases

ABCD altitude angle angles are equal base bisect bisector called chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder diagonals diameter diedral angles difference distance divide draw drawn equal equidistant equivalent exterior angle faces figure Find formed four geometrical given circle given line given point greater Hence homologous hypotenuse inches included inscribed intersecting isosceles triangle length less limit line joining measured median meet midpoints opposite sides parallel parallel lines parallelogram passing perimeter perpendicular plane polyedron polygon prism PROBLEM Proof PROPOSITION prove prove Hyp pyramid quadrilateral radii radius ratio rectangle regular polygon respectively right angles right triangle School segments sides similar sphere spherical triangle square straight line surface tangent THEOREM third transform triangle triangle are equal vertex vertices

### Popular passages

Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.

Page 180 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.

Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...

Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.

Page 328 - Every section of a sphere made by a plane is a circle.

Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.