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 184
... triangular portions ABO , of a polygon circumscribing a circle , is to the corresponding circular sec- tor , as the side AB of the polygon to the arc of the circle included between AO , BO . Cor . 2. Every circular arc is greater than ...
... triangular portions ABO , of a polygon circumscribing a circle , is to the corresponding circular sec- tor , as the side AB of the polygon to the arc of the circle included between AO , BO . Cor . 2. Every circular arc is greater than ...
Page 202
... is the area of a triangular field , two of whose sides AB and DB are 10 and 8 rods respectively , and the ratio of DB to the perpendicular DC = , 734 . 10X8X.734 58.72 , the area of the = triangle . 202 MENSURATION OF SUPERFICIES .
... is the area of a triangular field , two of whose sides AB and DB are 10 and 8 rods respectively , and the ratio of DB to the perpendicular DC = , 734 . 10X8X.734 58.72 , the area of the = triangle . 202 MENSURATION OF SUPERFICIES .
Page 204
... triangular field ABC , I measured a base line BD , until it met AC produced in D , 12 chains ; from the angles A and C , I then measured lines AF and CE perpendicular to BD , and found them to be 12 and 8 chains respectively . Required ...
... triangular field ABC , I measured a base line BD , until it met AC produced in D , 12 chains ; from the angles A and C , I then measured lines AF and CE perpendicular to BD , and found them to be 12 and 8 chains respectively . Required ...
Page 205
... triangular field ABC destitute of access , except by two ways , viz : by the lines BD terminating in the angle B , and CE in the angle C , perpendicular to each oth- er . I set out to determine its area ; and find by measuring , that ...
... triangular field ABC destitute of access , except by two ways , viz : by the lines BD terminating in the angle B , and CE in the angle C , perpendicular to each oth- er . I set out to determine its area ; and find by measuring , that ...
Page 25
... triangular , quadrangular , pentagonal , hexa- gonal , & c . when the base is a triangle , a quadrilateral , a pen- tagon , a hexagon , & c . 9. A prism whose base is a parallelogram , and which has all its faces parallelogram , is ...
... triangular , quadrangular , pentagonal , hexa- gonal , & c . when the base is a triangle , a quadrilateral , a pen- tagon , a hexagon , & c . 9. A prism whose base is a parallelogram , and which has all its faces parallelogram , is ...
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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.