First Lessons in Geometry: With Practical Applications in Mensuration, and Artificers' Work and Mechanics |
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Page 16
... Hence , a solid has three dimensions , a sur- face two , and a line one . A point has no dimensions , but position only . 9. Geometry treats of lines , surfaces , and solids . 10. A Demonstration is a course of reasoning which ...
... Hence , a solid has three dimensions , a sur- face two , and a line one . A point has no dimensions , but position only . 9. Geometry treats of lines , surfaces , and solids . 10. A Demonstration is a course of reasoning which ...
Page 19
... Hence , all right angles are equal to each other . 4. An acute angle is less than a right angle . Thus , DBC is an acute angle . 5. An obtuse angle is greater than a right angle . Thus , EBC is an obtuse angle . A B D B E B QUEST . - 2 ...
... Hence , all right angles are equal to each other . 4. An acute angle is less than a right angle . Thus , DBC is an acute angle . 5. An obtuse angle is greater than a right angle . Thus , EBC is an obtuse angle . A B D B E B QUEST . - 2 ...
Page 21
... Hence , one right angle contains 90 degrees , two right angles 180 degrees , three right angles 270 degrees , and four right angles 360 degrees . 10. One quarter of the circumference is called a quadrant , and contains 90 degrees . One ...
... Hence , one right angle contains 90 degrees , two right angles 180 degrees , three right angles 270 degrees , and four right angles 360 degrees . 10. One quarter of the circumference is called a quadrant , and contains 90 degrees . One ...
Page 25
... Hence , the perimeter of a polygon is the sum of all its sides . QUEST . - 8 . From the same point , how many perpendiculars can be drawn to a line ? If oblique lines be drawn , which will be the least ? Which the greatest ? 1. What is ...
... Hence , the perimeter of a polygon is the sum of all its sides . QUEST . - 8 . From the same point , how many perpendiculars can be drawn to a line ? If oblique lines be drawn , which will be the least ? Which the greatest ? 1. What is ...
Page 33
... Hence , a triangle is half a rectangle , having the same base and altitude . D A D FB QUEST . - 10 . What is the altitude of a parallelogram ? 11. What is the area of a parallelogram equal to ? If the base of a parallelogram be 10 feet ...
... Hence , a triangle is half a rectangle , having the same base and altitude . D A D FB QUEST . - 10 . What is the altitude of a parallelogram ? 11. What is the area of a parallelogram equal to ? If the base of a parallelogram be 10 feet ...
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Common terms and phrases
14 feet 20 feet ABCD altitude breadth called circle whose diameter circular sector circumfer circumference cone convex surface cubic feet cubic foot cumference cylinder decimal diagonal distance divide draw equilateral triangle EXAMPLES Explain the manner feet 6 inches figure find the area find the solidity frustum girt given angle given line given point heptagon hypothenuse inscribed square intersect line be drawn linear unit manner of inscribing measure Mensuration of Surfaces number of square parallel planes parallelogram pentagon perpendicular place one foot Practical Geometry.-Instruments Practical Geometry.-Problems prism PROBLEM protractor pyramid quadrilateral radius rectangle regular polygon Required the area rhombus right angled triangle Round Bodies RULE scale of chords scale of equal secant line segment similar polygons similar triangles slant height solid content solid feet Solids bounded specific gravity sphere square feet square rods square yards straight line tangent timber trapezoid
Popular passages
Page 35 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
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 82 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.
Page 142 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.
Page 84 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.
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 41 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.
Page 36 - The angles opposite the equal sides of an isosceles triangle are equal.
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.