Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration |
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Page 74
... quadrant AE = the quadrant AG , and because the arc FE the arc AH , the quadrant AE - arc FE - the quadrant AG - arc AH ( Ax . 3. ) Hence the arc AF - arc HG . And as the lines GE and ED are one continued straight line , meeting the two ...
... quadrant AE = the quadrant AG , and because the arc FE the arc AH , the quadrant AE - arc FE - the quadrant AG - arc AH ( Ax . 3. ) Hence the arc AF - arc HG . And as the lines GE and ED are one continued straight line , meeting the two ...
Page 177
... quadrant FADC , will be equivalent to the half of the second , or to the semicircle ABC . If the common segment ADCEA therefore be taken away , the remainders , that is to say , the triangle AEC on the one hand , and the lunule ABCDA on ...
... quadrant FADC , will be equivalent to the half of the second , or to the semicircle ABC . If the common segment ADCEA therefore be taken away , the remainders , that is to say , the triangle AEC on the one hand , and the lunule ABCDA on ...
Page 221
... quadrant . Ans . .019894 . Ex . 5. The area of a circular plantation is known to oc- cupy an acre and a half of ground , what must be the length of a line , which will strike the circle ? Ans . 48.072 yards . Ex . 6. In the midst of a ...
... quadrant . Ans . .019894 . Ex . 5. The area of a circular plantation is known to oc- cupy an acre and a half of ground , what must be the length of a line , which will strike the circle ? Ans . 48.072 yards . Ex . 6. In the midst of a ...
Page 223
... quadrant , whose radius is Ans . 1509.4675 . Ex . 2. What is the area of a semicircle , whose diameter is 32 . Ex . 3. If the arc ADB be 240 ° , and the radius of the circle 113 , what is the area of the sector ADBC . PROBLEM XVII . To ...
... quadrant , whose radius is Ans . 1509.4675 . Ex . 2. What is the area of a semicircle , whose diameter is 32 . Ex . 3. If the arc ADB be 240 ° , and the radius of the circle 113 , what is the area of the sector ADBC . PROBLEM XVII . To ...
Page 224
... quadrant of a circle , whose radius is 25 feet . Ans . 178.37 . Ex . 4. What is the area of the segment contained by an arc of 120 ° , if the radius is 2 feet . Ex . 5. What is the area of the segment , whose arc is 270 ° , when the ...
... quadrant of a circle , whose radius is 25 feet . Ans . 178.37 . Ex . 4. What is the area of the segment contained by an arc of 120 ° , if the radius is 2 feet . Ex . 5. What is the area of the segment , whose arc is 270 ° , when the ...
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield No preview available - 2015 |
Common terms and phrases
ABCD abscissa altitude axis bisect chord circle circular segment circum circumference circumscribing cone conjugate construction convex surface cosec cosine cube curve cylinder described diameter distance divided draw ellipse equal to half equation equivalent feet figure formed frustum Geom geometry given hence hyperbola hypothenuse inches inscribed inscribed sphere latus rectum length logarithm magnitude measured multiplied by one-third number of sides opposite ordinates parabola parallel parallelogram perimeter perpendicular plane polyedroid polyedron polygon portion prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon revoloid rhomboid right angled triangle right line root Scholium sector segment similar similar triangles sine slant height solid angle sphere spherical square straight line tangent THEOREM triangle ABC triangular triangular prism ungula vertex vertical virtual centre
Popular passages
Page 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 35 - The sum of any two sides of a triangle, is greater than the third side.
Page 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Page 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Page 211 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Page 48 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.