First Lessons in Geometry: With Practical Applications in Mensuration, and Artificers' Work and Mechanics |
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Page xi
... chords , and use 97-98 Protractor , and use 99-100 Practical problems 101-116 PART III . SECTION I. Mensuration of Surfaces General principles Area of a rectangle - Square or parallelogram Area of a Triangle Properties of right - angled ...
... chords , and use 97-98 Protractor , and use 99-100 Practical problems 101-116 PART III . SECTION I. Mensuration of Surfaces General principles Area of a rectangle - Square or parallelogram Area of a Triangle Properties of right - angled ...
Page 49
... chord of a circle , is a line drawn within a circle , and termi- nating in the circumference , but not passing through the centre . Thus , AB is a chord . A chord divides the circle into two unequal parts . 7. A segment of a circle , is ...
... chord of a circle , is a line drawn within a circle , and termi- nating in the circumference , but not passing through the centre . Thus , AB is a chord . A chord divides the circle into two unequal parts . 7. A segment of a circle , is ...
Page 53
... chord . Thus , the angle CAE , is measured by half the arc ADC ; and the angle CAB , by half the arc CFMA ... chord ? If the arc of the chord be 60 degrees , what will the angle formed by the tangent and chord be equal to ? Of the Circle ...
... chord . Thus , the angle CAE , is measured by half the arc ADC ; and the angle CAB , by half the arc CFMA ... chord ? If the arc of the chord be 60 degrees , what will the angle formed by the tangent and chord be equal to ? Of the Circle ...
Page 54
... chord . 22. In the same , or in equal cir- cles , chords which are equally dis- tant from the centre , are equal . Thus , if CA = CB , then will the chord FG chord DE . = F B E 23. If the chord DG is equal to the chord FH , they will be ...
... chord . 22. In the same , or in equal cir- cles , chords which are equally dis- tant from the centre , are equal . Thus , if CA = CB , then will the chord FG chord DE . = F B E 23. If the chord DG is equal to the chord FH , they will be ...
Page 56
... chords intersect each other the product , or rectangle of the parts of the one , is equal to the rectangle of the parts of the other . Thus , the two chords AB and CD , which intersect each other at E , give AEX EB CEXED . F C E QUEST ...
... chords intersect each other the product , or rectangle of the parts of the one , is equal to the rectangle of the parts of the other . Thus , the two chords AB and CD , which intersect each other at E , give AEX EB CEXED . F C E QUEST ...
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Common terms and phrases
12 feet 20 feet acres altitude bisect bounded by Planes breadth called centre of gravity chord circular sector circumfer circumference cone convex surface cubic feet cubic foot cubic inches cylinder decimal diagonals diameter distance divide draw equilateral triangle EXAMPLES Explain the manner feet 6 inches figure find the area find the solidity frustum given angle given line given point gles half hypothenuse intersect line be drawn linear unit lower base manner of inscribing Mensuration of Surfaces multiplied number of square parallel planes parallelogram parallelopipedon pentagon pentagonal pyramid perpendicular Practical Geometry.-Problems PROBLEM pulley pyramid radius rectangle regular polygon regular solids Required the area rhombus right angled triangle Round Bodies RULE scale of equal secant line segment similar polygons similar triangles slant height solid content solid feet Solids bounded specific gravity sphere square feet square yards straight line tangent thickness upper base 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.