Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of Projection |
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Page 68
... original progression 1 ,,, and inserting first one harmonical mean between its terms , we get the progression 1 ,,,, ; se- condly , two harmonical means between its terms , 1 , 4 , † , † , † , TT , ; and thirdly , three har- monical ...
... original progression 1 ,,, and inserting first one harmonical mean between its terms , we get the progression 1 ,,,, ; se- condly , two harmonical means between its terms , 1 , 4 , † , † , † , TT , ; and thirdly , three har- monical ...
Page 74
... original ratio ; and so on . Let these successive ratios be written one after another in the order in which they are derived : ( a ) R : P ; ( b ) P : 2 P + R , ( c ) 2 P + R : 5 P + 2R ; ( d ) 5 P + 2R : 12 P + 5 R ; ( e ) 12 P +5 R ...
... original ratio ; and so on . Let these successive ratios be written one after another in the order in which they are derived : ( a ) R : P ; ( b ) P : 2 P + R , ( c ) 2 P + R : 5 P + 2R ; ( d ) 5 P + 2R : 12 P + 5 R ; ( e ) 12 P +5 R ...
Page 86
... original posi- tion CA , is brought successively into the positions C Q , C Q 2 , C Q ,, and thence again , continuing its revolution , a second time into the same positions CA , CQ , CQ2 , CQ ,, and so on . Then it is evident that the ...
... original posi- tion CA , is brought successively into the positions C Q , C Q 2 , C Q ,, and thence again , continuing its revolution , a second time into the same positions CA , CQ , CQ2 , CQ ,, and so on . Then it is evident that the ...
Page 102
... original figure above the circle , so that , were there such an excess , a rectilineal figure might be found greater than the circle , and yet of less perimeter , which is im- possible . This method will not , how- ever , carry us any ...
... original figure above the circle , so that , were there such an excess , a rectilineal figure might be found greater than the circle , and yet of less perimeter , which is im- possible . This method will not , how- ever , carry us any ...
Page 146
... original pyramid ; the second is equal ( 30. ) to a pyramid BCDE , upon the same base CDE , and having its vertex B in the same line AB parallel ( 10. ) to the base ; and the third is equal to a pyramid BDEF , upon the same base D E F ...
... original pyramid ; the second is equal ( 30. ) to a pyramid BCDE , upon the same base CDE , and having its vertex B in the same line AB parallel ( 10. ) to the base ; and the third is equal to a pyramid BDEF , upon the same base D E F ...
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.