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

### From inside the book

Page ix

OF ANGLES .

19 20 SECTION III . Parallel lines - Oblique lines . Parallel cut by a third line .

Perpendicular and oblique lines : 23 24 25 . SECTION IV . Plane Figures ...

Different ...

OF ANGLES .

**Right angle**- Acute angle - Obtuse angle Measures of angles . 1819 20 SECTION III . Parallel lines - Oblique lines . Parallel cut by a third line .

Perpendicular and oblique lines : 23 24 25 . SECTION IV . Plane Figures ...

Different ...

Page 18

Of

5. Things which are halves of the same thing are equal ... An

read by placing the letter at QUEST . ... Of

Of

**Angles**. 4. Things which are double of the same thing are equal to each other .5. Things which are halves of the same thing are equal ... An

**angle**is generallyread by placing the letter at QUEST . ... Of

**Angles**—**Right**, Acute , and Obtuse . Page 19

Of

the

perpendicular to another , when it inclines no more to the one side than to the

other .

Of

**Angles**—**Right**, Acute , and Obtuse . the vertex in the middle . Thus , we saythe

**angle**CAB . We may , however , say simply , the**angle**A. 2. One line isperpendicular to another , when it inclines no more to the one side than to the

other .

Page 21

Of Angles . we draw CF through the point of division marked 80 , it will make with

CB an angle equal to 80 degrees . ... Hence , one

degrees , two

four right ...

Of Angles . we draw CF through the point of division marked 80 , it will make with

CB an angle equal to 80 degrees . ... Hence , one

**right angle**contains 90degrees , two

**right angles**180 degrees , three**right angles**270 degrees , andfour right ...

Page 22

Of Angles . 11. If a straight line EB meets E E another straight line AC , the sum of

the angles ABE and EBC , will be equal to two

angles are measured by half the circumference . Andif there be several angles ...

Of Angles . 11. If a straight line EB meets E E another straight line AC , the sum of

the angles ABE and EBC , will be equal to two

**right angles**, since these A twoangles are measured by half the circumference . Andif there be several angles ...

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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.