## First Lessons in Geometry: With Practical Applications in Mensuration, and Artificers' Work and Mechanics |

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Results 1-5 of 28

Page 15

A Straight Line , is the shortest

is a straight line , and the shortest

which changes its direction at every point . Thus , ABC is a curve line . B A The ...

A Straight Line , is the shortest

**distance**from one point to another . A -B Thus , ABis a straight line , and the shortest

**distance**from A to B. 4. A Curve Line , is onewhich changes its direction at every point . Thus , ABC is a curve line . B A The ...

Page 23

Two straight lines are said to be parallel when they are at the same

each other at every point . Parallel lines will never meet each other . 2. Two

curves are said to be parallel or concentric , when they are at the same

from ...

Two straight lines are said to be parallel when they are at the same

**distance**fromeach other at every point . Parallel lines will never meet each other . 2. Two

curves are said to be parallel or concentric , when they are at the same

**distance**from ...

Page 33

The altitude of a parallelogram is the perpendicular

parallel sides . Thus , EB is the altitude of the parallelogram ABCD . А 11. The

area of a parallelogram is equal to its base multiplied by its altitude . Thus , the

area ...

The altitude of a parallelogram is the perpendicular

**distance**between two of itsparallel sides . Thus , EB is the altitude of the parallelogram ABCD . А 11. The

area of a parallelogram is equal to its base multiplied by its altitude . Thus , the

area ...

Page 54

The

perpendicular to the chord . D 22. In the same , or in equal cir F cles , chords

which are equally disB tant from the centre , are equal . С Thus , if CA = CB , then

will the E ...

The

**distance**from the centre of a circle to a chord , is measured on aperpendicular to the chord . D 22. In the same , or in equal cir F cles , chords

which are equally disB tant from the centre , are equal . С Thus , if CA = CB , then

will the E ...

Page 62

A perpendicular is the shortest

be P drawn to the plane , those nearest the perpendicular will be less than D

those more remote . Thus , if PA be perpendicular to the plane DC , it will be the ...

A perpendicular is the shortest

**distance**from a point to a plane . If oblique linesbe P drawn to the plane , those nearest the perpendicular will be less than D

those more remote . Thus , if PA be perpendicular to the plane DC , it will be the ...

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12 feet 20 feet ABCD acres altitude attraction base body bounded breadth brick called centre chord circle circumference cone contain convex surface cubic feet cubic inches curve cylinder decimal describe diameter dimensions distance divided divisions draw drawn equal EXAMPLES Explain the manner face fall feet 6 inches figure find the area find the solidity foot frustum Geometry girt give given given point greater half Hence hexagon inches inscribed intersect kind known length less lever marked measure Mechanical Mensuration of Surfaces move Multiply opposite parallel pass pentagon perpendicular piece plane polygon prism PROBLEM pulley pyramid radius rectangle regular right angles ring rods Round Bodies RULE scale segment side similar solid feet solidity specific gravity sphere square feet straight line tangent thickness timber triangle unit weight

### Popular passages

Page 20 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Page 32 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.

Page 40 - Similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF be two similar triangles...

Page 82 - A zone is a portion of the surface of a sphere included between two parallel planes.

Page 235 - An equilibrium is produced in all the levers, when the weight multiplied by its distance from the fulcrum is equal to the product of the power multiplied by its distance from the fulcrum. That...

Page 84 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.

Page 34 - The area of a triangle is equal to half the product of the base and height.

Page 35 - 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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

Page 20 - For this purpose it is divided into 360 equal parts, called degrees, each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. The degrees, minutes, and seconds, are marked thus, °, ', " ; and 9° 18' 10", are read, 9 degrees, 18 minutes, and 10 seconds.

Page 83 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.