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 55
... rectangle and square ( see Defini- tions ) all the angles are right , and in the latter all the sides are equal . Cor . 3. The diagonal divides a rhomboid into two equiva- lent triangles . Cor . 4. Parallels included between two other ...
... rectangle and square ( see Defini- tions ) all the angles are right , and in the latter all the sides are equal . Cor . 3. The diagonal divides a rhomboid into two equiva- lent triangles . Cor . 4. Parallels included between two other ...
Page 82
... rectangle ; if , in addition to this , the sides are equal , it will be a square . PROBLEM XIV . To find the centre of a given circle , or arc . Take three points , A , B , C , any where in the circumference , or the arc ; draw AB , BC ...
... rectangle ; if , in addition to this , the sides are equal , it will be a square . PROBLEM XIV . To find the centre of a given circle , or arc . Take three points , A , B , C , any where in the circumference , or the arc ; draw AB , BC ...
Page 86
... figure contains some other area , that is assumed for its mea- suring unit . 8. Figures have equal areas , when they contain the same measuring unit an equal number of times . 9. A rectangle is said to be contained by any.
... figure contains some other area , that is assumed for its mea- suring unit . 8. Figures have equal areas , when they contain the same measuring unit an equal number of times . 9. A rectangle is said to be contained by any.
Page 87
... rectangle AB- CD is contained by the lines AB and BC , or by BC and CD . B C D A rectangle , or polygon , may , for the sake of brevity , be designated by two letters at its opposite angles , as AC or BD ; and the rectangle contained by ...
... rectangle AB- CD is contained by the lines AB and BC , or by BC and CD . B C D A rectangle , or polygon , may , for the sake of brevity , be designated by two letters at its opposite angles , as AC or BD ; and the rectangle contained by ...
Page 88
... rectangle of equal base and altitude . Cor . 4. A line bisecting the opposite sides of a rhomboid divides the rhomboid into two equal parts . Scholium . It is very evident that the converse of 88 ELEMENTS OF GEOMETRY .
... rectangle of equal base and altitude . Cor . 4. A line bisecting the opposite sides of a rhomboid divides the rhomboid into two equal parts . Scholium . It is very evident that the converse of 88 ELEMENTS OF GEOMETRY .
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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.