Geometry, plane, solid, and spherical. To which is added, in an appendix, the theory of projection [&c. By P. Morton].1830 |
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Geometry, Plane, Solid, and Spherical. to Which Is Added, in an Appendix ... Pierce Morton No preview available - 2015 |
Geometry, Plane, Solid, and Spherical. to Which Is Added, in an Appendix ... Pierce Morton No preview available - 2018 |
Common terms and phrases
ABCD adjacent angles altitude angles equal apothem axis base BC bisected centre chord circum circumference circumscribed coincide common measure common section compounded conic section contained convex surface cumference curve cylinder demonstration diameter dihedral angles distance divided draw drawn ellipse equal angles equimultiples ference fore four magnitudes frustum given point given straight line gles harmonical harmonical mean Hence hyperbola hypotenuse inscribed join meet parabola parallel parallelogram parallelopiped pass pendicular perimeter perpendicular plane point G prism Prob produced projection PROP proposition pyramid quadrant quadrilateral radii radius rallel rectangle rectilineal figure regular polygon respectively right angles Scholium scribed segment sides A B similar solid angles solid content sphere spherical angle spherical arc spherical triangle square tangent third three sides touch triangle ABC vertex vertical
Popular passages
Page 6 - second part of.) Hence, 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, the equal sides being opposite to equal angles in each, the two triangles shall be equal in
Page 4 - The vertical angles EHL, FHK are likewise equal to one another (3.). Therefore, the triangles HEL and HFK having two angles of the one equal to two angles of the other, each to each, and their sides HE, HF, which lie between the equal angles, also equal to one another, are equal in every respect (5.). Therefore, the angle
Page xiv - If two triangles have two angles of the one equal to two angles of the other, each to each, and likewise the interjacent* sides equal ; their other sides shall be equal, each to each, viz. those to which the equal angles are opposite, and the third angle of the one shall be equal to the third angle of the other.
Page 54 - Cor. 3. (Eue. vi. 14.) And, in the same manner, it may be shown, that any two parallelograms which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another ; and conversely.
Page 53 - EF, which have one angle of the one equal to one angle of the other, are to one another in the ratio which is compounded of the ratios of the sides about the equal angles. For if the equal angles be made to coincide, as at
Page 119 - equal to one another, the bases PD, P dare likewise equal (1.4.). Lastly, therefore, because the triangles PAD, P Ad have the three sides of the one equal to the three sides of the other, each to each, the angles PAD, P Ad are equal to one another, and (I def.
Page xvi - Therefore, &c. PROP. 10. (Eue. i. 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let
Page xi - 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. This point is called the centre of the circle ; and the distance from the centre to the circumference is called the
Page 119 - are equal to the two AB, BG, each to each, and the included angles right angles, AF is equal to AG (I. 4.). Therefore, lastly, because the triangles AHF, AH G have the three sides of the one equal to the three sides of the other, each to each, the angle AHF is equal to the angle
Page 182 - С shall likewise be equal to the sides DE, DF and EF, each to each. For, if the polar triangles A' B' C', D' E' F' be described, they will have the three sides of the one equal to the three sides of the other, each to each, because every two corresponding sides, as A' B