Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of Projection |
From inside the book
Results 1-5 of 100
Page 27
... loci , to be noticed hereafter ( in Book III . Sect . 6 ) , and which may here be explained as circumscribing the range , if it be limited , within which every particular datum confines the solu- tion of the problem ; for it is obvious ...
... loci , to be noticed hereafter ( in Book III . Sect . 6 ) , and which may here be explained as circumscribing the range , if it be limited , within which every particular datum confines the solu- tion of the problem ; for it is obvious ...
Page 106
... Loci . Def . 14. A locus in Plane Geometry is a straight line , circle , or plane curve , every point of which , and none else in that plane , satisfies a certain condition . The nature and use of loci will be readily apprehended from ...
... Loci . Def . 14. A locus in Plane Geometry is a straight line , circle , or plane curve , every point of which , and none else in that plane , satisfies a certain condition . The nature and use of loci will be readily apprehended from ...
Page 107
... locus ; when the cir- cumference of a circle , it is called a plane locus ; when any other curve , it is said to be of higher dimensions than the circle . The following propositions afford ex- amples of the two first only ; and , the ...
... locus ; when the cir- cumference of a circle , it is called a plane locus ; when any other curve , it is said to be of higher dimensions than the circle . The following propositions afford ex- amples of the two first only ; and , the ...
Page 108
... locus of all points dividing them in the same given ratio Let A B be any straight line drawn from A to B C , and divided in the given ratio in the point D ; and let P be a point B in the locus . Then , because AP is to PC in the same ...
... locus of all points dividing them in the same given ratio Let A B be any straight line drawn from A to B C , and divided in the given ratio in the point D ; and let P be a point B in the locus . Then , because AP is to PC in the same ...
Page 109
... locus . Bisect AB in D , and join PD . Then , because the base AB of the triangle PAB is bisected in D , the sum of the E A D B squares of PA , PB is equal to twice the square of PD , together with twice the square of DA ( I. 40. ) But ...
... locus . Bisect AB in D , and join PD . Then , because the base AB of the triangle PAB is bisected in D , the sum of the E A D B squares of PA , PB is equal to twice the square of PD , together with twice the square of DA ( I. 40. ) But ...
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.