First Lessons in Geometry: With Practical Applications in Mensuration, and Artificers' Work and Mechanics |
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Page 28
... right angled triangle , which has one right angle . In the right angled triangle BAC , the side BC op- posite the right angle , is called the hy- pothenuse . B 13. The base of a triangle is the side on which it stands . Thus , BA is the ...
... right angled triangle , which has one right angle . In the right angled triangle BAC , the side BC op- posite the right angle , is called the hy- pothenuse . B 13. The base of a triangle is the side on which it stands . Thus , BA is the ...
Page 29
... angles right angles , and its opposite sides equal and parallel . Third . The parallelogram , which has its opposite sides equal and parallel , but its angles not right angles . Fourth . The rhombus , which has all its sides equal , and ...
... angles right angles , and its opposite sides equal and parallel . Third . The parallelogram , which has its opposite sides equal and parallel , but its angles not right angles . Fourth . The rhombus , which has all its sides equal , and ...
Page 37
... . If one side of a triangle be produced out , what will the outward angle be equal to ? 8. What is the sum of the three angles of any triangle equal to ? Properties of the Triangle . 9. In every right angled 4 PART I. -SECTION VI . 37.
... . If one side of a triangle be produced out , what will the outward angle be equal to ? 8. What is the sum of the three angles of any triangle equal to ? Properties of the Triangle . 9. In every right angled 4 PART I. -SECTION VI . 37.
Page 38
... right angled triangle , the sum of the two acute angles is equal to 90 degrees . Thus , B + C 90 degrees ; This is evident , since A + B + C 180 degrees , and A 90 degrees . = B 10. In every right an- gled triangle , the square ...
... right angled triangle , the sum of the two acute angles is equal to 90 degrees . Thus , B + C 90 degrees ; This is evident , since A + B + C 180 degrees , and A 90 degrees . = B 10. In every right an- gled triangle , the square ...
Page 43
... angles of any polygon is equal to twice as many right angles , wanting four , as the figure has sides . Thus , if the polygon has five sides , we have = E B A + B + C + D + E = 10 right angles - 4 right angles 6 right angles . 7. If the ...
... angles of any polygon is equal to twice as many right angles , wanting four , as the figure has sides . Thus , if the polygon has five sides , we have = E B A + B + C + D + E = 10 right angles - 4 right angles 6 right angles . 7. If the ...
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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.