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 |
From inside the book
Results 1-5 of 99
Page 10
... less than the latter . Thus , AB indicates that the quantity repre- sented by A is greater than that represented by B : by A < B is implied that A is less than B. 3. The sign is called plus : it indicates addition . 4. The sign is ...
... less than the latter . Thus , AB indicates that the quantity repre- sented by A is greater than that represented by B : by A < B is implied that A is less than B. 3. The sign is called plus : it indicates addition . 4. The sign is ...
Page 15
... less ; and the less is , in this case , called a submultiple of the greater . 17. Equimultiples of two quantities are the products which arise from multiplying the quantities by the same number ; thus AXm , BXm , are equimultiples of A ...
... less ; and the less is , in this case , called a submultiple of the greater . 17. Equimultiples of two quantities are the products which arise from multiplying the quantities by the same number ; thus AXm , BXm , are equimultiples of A ...
Page 16
... less of P's than A , as B contains units . Hence the P's contained in their difference are equal to the difference of the P's con- tained in the two magnitudes , viz . Q - q : therefore the dif- ference of the two magnitudes is measured ...
... less of P's than A , as B contains units . Hence the P's contained in their difference are equal to the difference of the P's con- tained in the two magnitudes , viz . Q - q : therefore the dif- ference of the two magnitudes is measured ...
Page 17
... less than B ; let C be in like manner taken as often as pos- sible from B , leaving a remainder D less than C ; now let D be in a similar way taken as often as possible from C , leav- ing a remainder E less than D , and so on till no ...
... less than B ; let C be in like manner taken as often as pos- sible from B , leaving a remainder D less than C ; now let D be in a similar way taken as often as possible from C , leav- ing a remainder E less than D , and so on till no ...
Page 30
... less , as the lines forming the angles are more or less inclined or opened , and like other magni- tudes or quantities are susceptible of addition , subtraction , multiplication and division . Thus the angle ABD is the sum of the two ...
... less , as the lines forming the angles are more or less inclined or opened , and like other magni- tudes or quantities are susceptible of addition , subtraction , multiplication and division . Thus the angle ABD is the sum of the two ...
Other editions - View all
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.