Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of ProjectionBaldwin and Cradock, 1830 - 272 sider |
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Side 22
... position of their parts , the square of the hypotenuse . It will be readily apprehended from the follow- ing outline . BAC is a triangle , having the angle at A a right angle : upon the hypo- tenuse B C is described the square BCDE ...
... position of their parts , the square of the hypotenuse . It will be readily apprehended from the follow- ing outline . BAC is a triangle , having the angle at A a right angle : upon the hypo- tenuse B C is described the square BCDE ...
Side 42
... positions of this Section will be re - stated , and such as have been referred to def . [ 7 ] , will have to be reconsidered with reference to a more general definition . A similar consideration will be found to have directed the ...
... positions of this Section will be re - stated , and such as have been referred to def . [ 7 ] , will have to be reconsidered with reference to a more general definition . A similar consideration will be found to have directed the ...
Side 45
... position , that if two ratios be equal It appears , therefore , from the pro- to one another ( and therefore com- pounded of equal ratios having any or- der in the composition of each ) , and if any of the equal ratios be subducted or ...
... position , that if two ratios be equal It appears , therefore , from the pro- to one another ( and therefore com- pounded of equal ratios having any or- der in the composition of each ) , and if any of the equal ratios be subducted or ...
Side 46
... position . Therefore , B ' cannot be less than B. Again , if B ' be supposed greater than B , take A ' such that A ' : B ' :: A : B. Then , because B is less than B ' , A is less than A ' ( [ 18 ] ) , as by some difference a . And ...
... position . Therefore , B ' cannot be less than B. Again , if B ' be supposed greater than B , take A ' such that A ' : B ' :: A : B. Then , because B is less than B ' , A is less than A ' ( [ 18 ] ) , as by some difference a . And ...
Side 65
... position . Therefore , alternando ( 19. ) BA - AC : BA + AC :: ED - DF : ED + DF : and , by sum and difference ( 24 . Cor . 2. ) 2 BA : 2AC :: 2ED : 2 DF , that is , ( 17.Cor . 2. ) BA : AC :: ED : DF . Therefore , & c . Cor . If DE be ...
... position . Therefore , alternando ( 19. ) BA - AC : BA + AC :: ED - DF : ED + DF : and , by sum and difference ( 24 . Cor . 2. ) 2 BA : 2AC :: 2ED : 2 DF , that is , ( 17.Cor . 2. ) BA : AC :: ED : DF . Therefore , & c . Cor . If DE be ...
Andre utgaver - Vis alle
Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ... Pierce Morton Uten tilgangsbegrensning - 1835 |
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Ingen forhåndsvisning tilgjengelig - 2023 |
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Ingen forhåndsvisning tilgjengelig - 2013 |
Vanlige uttrykk og setninger
A B C a² b² ABCD altitude asymptote axes axis base bisected centre chord circle circumference circumscribed co-ordinates common section conic section contained convex surface curve cylinder describe diameter difference dihedral angle distance divided draw drawn ellipse equal angles equation frustum given line given point given straight line gles greater hence hyperbola hypotenuse inscribed intersection join Latus Rectum less likewise locus magnitudes meet parabola parallel parallelogram parallelopiped pass pendicular perimeter perpendicular perspective projection pole prism produced projection PROP pyramid radii radius ratio rectangle rectangular rectilineal figure regular polygon right angles Scholium segment similar solid angles solid content sphere spherical angle spherical arc spherical triangle square tangent tion touch triangle ABC vertex vertical y₁
Populære avsnitt
Side 196 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 64 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 20 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles ; and upon BC, one of the sides containing it, let fall the perpendicular...
Side 10 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 189 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Side 1 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 84 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Side 78 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Side 79 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Side 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.