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
... means of a train of reasoning called a demonstration A Demonstration is direct , when the truth is inferred di- rectly from the premises , as the conclusion of a regular se- ries of inductions . A Demonstration is indirect , when the ...
... means of a train of reasoning called a demonstration A Demonstration is direct , when the truth is inferred di- rectly from the premises , as the conclusion of a regular se- ries of inductions . A Demonstration is indirect , when the ...
Page 11
... means the square root of 2 ; AXB or ✓ ( AXB ) means the square root of the product of A and B. 11. The symbol .. is used to denote the word hence or therefore ; indicating a conclusion , depending on the fore- going premises . AXIOMS ...
... means the square root of 2 ; AXB or ✓ ( AXB ) means the square root of the product of A and B. 11. The symbol .. is used to denote the word hence or therefore ; indicating a conclusion , depending on the fore- going premises . AXIOMS ...
Page 14
... means . 10. Of four proportional quantities the first and third are called the antecedents , and the second and fourth the conse- quents ; and the last is said to be a fourth proportional to the other three taken in order . Antecedents ...
... means . 10. Of four proportional quantities the first and third are called the antecedents , and the second and fourth the conse- quents ; and the last is said to be a fourth proportional to the other three taken in order . Antecedents ...
Page 18
... means be increased or di- minished till it will express any given magnitude . ( Post . 5 . See also notes ) . But since a quantity requiring an expression in an indefi- nite number of terms , cannot be definitely expressed in visi- ble ...
... means be increased or di- minished till it will express any given magnitude . ( Post . 5 . See also notes ) . But since a quantity requiring an expression in an indefi- nite number of terms , cannot be definitely expressed in visi- ble ...
Page 20
... means . Let A , B , C , D be four magnitudes which are in propor- tion , and Q , q and Q , q ' their numerical representatives when compared with the unit P ; then if Q : q :: Q ' : q ' , so will QXqQXq . For since the quantities are in ...
... means . Let A , B , C , D be four magnitudes which are in propor- tion , and Q , q and Q , q ' their numerical representatives when compared with the unit P ; then if Q : q :: Q ' : q ' , so will QXqQXq . For since the quantities are in ...
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.