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 29
... right , or curved , or mixed of these two . 8. A right line , or straight line , lies all in the same direc- tion between its extreme points , and if traced by a point , the point ... line . 11. If two lines meet each other in a point.
... right , or curved , or mixed of these two . 8. A right line , or straight line , lies all in the same direc- tion between its extreme points , and if traced by a point , the point ... line . 11. If two lines meet each other in a point.
Page 30
... lines forming that angle , but altogether upon their relative position or in- clination . 13. One right line is said to be perpendicular to another , when it makes with it equal adjacent an- gles A perpendicu- lar at the extremity of a line ...
... lines forming that angle , but altogether upon their relative position or in- clination . 13. One right line is said to be perpendicular to another , when it makes with it equal adjacent an- gles A perpendicu- lar at the extremity of a line ...
Page 31
... right line is meant the perpendicular from that point to the line ; and one line is said to be equidistant from another , when every point in the one is equidistant from the other . 17. Right lines are parallel , when they are at the ...
... right line is meant the perpendicular from that point to the line ; and one line is said to be equidistant from another , when every point in the one is equidistant from the other . 17. Right lines are parallel , when they are at the ...
Page 33
... right line which joins the vertices of two oppo- site angles of a quadrilateral is called a diagonal . Thus the line AC joining the vertices of the opposite angles DAB , DCB , of the quadrilateral ... right line AC or 5 BOOK II . 33.
... right line which joins the vertices of two oppo- site angles of a quadrilateral is called a diagonal . Thus the line AC joining the vertices of the opposite angles DAB , DCB , of the quadrilateral ... right line AC or 5 BOOK II . 33.
Page 35
... right angle BCE ; hence the sum of the two angles ACD and BCD is equal to two right angles . Cor . 1. If one of the angles ACD , BCD , is right , the other is right also . Cor . 2. If the line DE is perpendicu- D lar to AB ...
... right angle BCE ; hence the sum of the two angles ACD and BCD is equal to two right angles . Cor . 1. If one of the angles ACD , BCD , is right , the other is right also . Cor . 2. If the line DE is perpendicu- D lar to AB ...
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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 arithmetical progression 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 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.