Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of Projection |
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Page 31
... fourth . The ratio of one magnitude to another is independent of the kind of magnitudes compared ; for it is obvious that one may contain the other , or the sixth , or twelfth , or hundredth part of the other the same number of times ...
... fourth . The ratio of one magnitude to another is independent of the kind of magnitudes compared ; for it is obvious that one may contain the other , or the sixth , or twelfth , or hundredth part of the other the same number of times ...
Page 32
... fourth ; or , which is the same thing , if the ratios of the first to the second , and of the third to the fourth be expressed by the same terms ; the first is said to have to the second the same ratio which the third has to the fourth ...
... fourth ; or , which is the same thing , if the ratios of the first to the second , and of the third to the fourth be expressed by the same terms ; the first is said to have to the second the same ratio which the third has to the fourth ...
Page 33
... fourth , are expressed by the same terms , and the two rectangles , and their two bases , are proportionals . In the preceding , and in every other instance of commensurable proportion- als , the first two , and the second two , have a ...
... fourth , are expressed by the same terms , and the two rectangles , and their two bases , are proportionals . In the preceding , and in every other instance of commensurable proportion- als , the first two , and the second two , have a ...
Page 34
... fourth , and so on . Magni- tudes A , B , C , D , & c . which are in con- tinued proportion , may be thus written , A : B : C : D : & c . The magnitudes of such a series are said to be in geometrical progression · and B , C , are called ...
... fourth , and so on . Magni- tudes A , B , C , D , & c . which are in con- tinued proportion , may be thus written , A : B : C : D : & c . The magnitudes of such a series are said to be in geometrical progression · and B , C , are called ...
Page 37
... fourth , and so on to the last , all the magnitudes shall be commensurable . Cor . 2. If two magnitudes be com- mensurable with one another , and if one of them be incommensurable with a third magnitude , the other shall like- wise be ...
... fourth , and so on to the last , all the magnitudes shall be commensurable . Cor . 2. If two magnitudes be com- mensurable with one another , and if one of them be incommensurable with a third magnitude , the other shall like- wise be ...
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.