Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of Projection |
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Page 1
... syl- lable Def . or Ax . The most important definitions only , which are taken from Euclid , and stated in nearly the same words , are here referred to . B In others : thus , the angle B A C Definitions 2 First theorems.
... syl- lable Def . or Ax . The most important definitions only , which are taken from Euclid , and stated in nearly the same words , are here referred to . B In others : thus , the angle B A C Definitions 2 First theorems.
Page 3
... referred to by the name of POSTULATES . * passes through two given points , A , B. 1. A straight line , which joins or B 2. A circle , which is described from a given centre , C , with a given radius , CA. Things required ; from the ...
... referred to by the name of POSTULATES . * passes through two given points , A , B. 1. A straight line , which joins or B 2. A circle , which is described from a given centre , C , with a given radius , CA. Things required ; from the ...
Page 12
... referred to the general principle of homo- one another , are equal in every respect geneity . Of this it is unnecessary to say more in this place , than that it teaches us in the present ( 5. ) . Therefore , the angle HLE is instance ...
... referred to the general principle of homo- one another , are equal in every respect geneity . Of this it is unnecessary to say more in this place , than that it teaches us in the present ( 5. ) . Therefore , the angle HLE is instance ...
Page 42
... referred to def . [ 7 ] as they may mensurable proportionals , they may , at least , as obvi- be derived from other propositions . The connected demonstrations have in this case been preferred with a view to the next Section , where ...
... referred to def . [ 7 ] as they may mensurable proportionals , they may , at least , as obvi- be derived from other propositions . The connected demonstrations have in this case been preferred with a view to the next Section , where ...
Page 45
... referred to in the demonstra- tions of Prop . [ 26 ] and [ 27 ] . It follows that a similar rule may be observed with regard to any number of ratios which are compounded according to Def . 12 ; viz . B , C will contain , also , by the.
... referred to in the demonstra- tions of Prop . [ 26 ] and [ 27 ] . It follows that a similar rule may be observed with regard to any number of ratios which are compounded according to Def . 12 ; viz . B , C will contain , also , by the.
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.