Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of Projection |
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Page vi
... pass two different straight lines , each of which is parallel to the same straight line . " The converse part of Prop . 14 , viz . that " parallel straight lines are at right angles to the same straight line , " will then be ...
... pass two different straight lines , each of which is parallel to the same straight line . " The converse part of Prop . 14 , viz . that " parallel straight lines are at right angles to the same straight line , " will then be ...
Page 6
... pass through the vertex A , let this perpendicular , if possible , cut one of the sides as A B in E , and join E C. Then , because the tri- angles ED B , EDC have two sides of the one equal to two sides of the other , each to each , and ...
... pass through the vertex A , let this perpendicular , if possible , cut one of the sides as A B in E , and join E C. Then , because the tri- angles ED B , EDC have two sides of the one equal to two sides of the other , each to each , and ...
Page 38
... pass on to that Section , or rather , to the concluding Scholium of the present one ; by which he will omit nothing that will be cited in the future pages of this treatise . On the other hand , it is recommended to beginners , and such ...
... pass on to that Section , or rather , to the concluding Scholium of the present one ; by which he will omit nothing that will be cited in the future pages of this treatise . On the other hand , it is recommended to beginners , and such ...
Page 58
... pass through the vertex of the triangle . Let A B C be a triangle , and let the straight line D E , which is drawn pa rallel to the base B C , cut the sides A B , AC in the points D , E respectively : then if any straight line AF be ...
... pass through the vertex of the triangle . Let A B C be a triangle , and let the straight line D E , which is drawn pa rallel to the base B C , cut the sides A B , AC in the points D , E respectively : then if any straight line AF be ...
Page 59
... passes through A. Therefore , & c . Cor . 1. If two parallel straight lines be cut by any number of straight lines which pass through the same point , they shall be similarly divided in the points of section . Cor . 2. It has been seen ...
... passes through A. Therefore , & c . Cor . 1. If two parallel straight lines be cut by any number of straight lines which pass through the same point , they shall be similarly divided in the points of section . Cor . 2. It has been seen ...
Other editions - View all
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton No preview available - 2023 |
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton No preview available - 2013 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.