Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of ProjectionBaldwin and Cradock, 1830 - 272 σελίδες |
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Σελίδα vi
... demonstration of the converse part of Book I. Prop . 14. , is attended with a difficulty which is stated at some length in page 11 , as we have been anxious that the student should be fully aware of its existence . It will be better ...
... demonstration of the converse part of Book I. Prop . 14. , is attended with a difficulty which is stated at some length in page 11 , as we have been anxious that the student should be fully aware of its existence . It will be better ...
Σελίδα 3
... demonstration , or course of reasoning ; -And , 4 ° . the conclusion , asserting that the thing required has been ... demonstrating merely the existence of the points and lines required in its enunciation , it becomes , for our purposes ...
... demonstration , or course of reasoning ; -And , 4 ° . the conclusion , asserting that the thing required has been ... demonstrating merely the existence of the points and lines required in its enunciation , it becomes , for our purposes ...
Σελίδα 4
... demonstrating the propositions of the following sections , and are therefore here premised : - AXIOMS . * -- 1. Things , which are equal to the same , are equal to one another . 2. If equals be added to equals , the wholes are equal . 3 ...
... demonstrating the propositions of the following sections , and are therefore here premised : - AXIOMS . * -- 1. Things , which are equal to the same , are equal to one another . 2. If equals be added to equals , the wholes are equal . 3 ...
Σελίδα 11
... demonstration which is said , and with truth , to characterize every other part of Geometry . Of the two particulars which have been assumed , one indeed , viz . , that which regards the unlimited di- vergency of cutting lines , seems ...
... demonstration which is said , and with truth , to characterize every other part of Geometry . Of the two particulars which have been assumed , one indeed , viz . , that which regards the unlimited di- vergency of cutting lines , seems ...
Σελίδα 12
... demonstration itself rests upon the converse part of Prop . 14. , which is here in question . The reader must not imagine , therefore , that the above assumption is at ail assisted by that demonstration . PROP . 15. ( Euc . i . 27 , 28 ...
... demonstration itself rests upon the converse part of Prop . 14. , which is here in question . The reader must not imagine , therefore , that the above assumption is at ail assisted by that demonstration . PROP . 15. ( Euc . i . 27 , 28 ...
Άλλες εκδόσεις - Προβολή όλων
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.