Solid and Spherical Geometry and Conic Sections: Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the Solid and Spherical Geometry of Playfair ...William and Robert Chambers and sold by all booksellers, 1837 - 164 páginas |
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Página 8
... consequently AF is perpendicular to GH ; and AF is also perpendicular to DE ; therefore AF is perpendicular to each of the straight lines GH , DE . But if a straight line stands at right angles to each of two straight lines in the point ...
... consequently AF is perpendicular to GH ; and AF is also perpendicular to DE ; therefore AF is perpendicular to each of the straight lines GH , DE . But if a straight line stands at right angles to each of two straight lines in the point ...
Página 12
... consequently it is perpendicular to CE . Where- fore ABF is a right angle ; but GFB is likewise a right angle ; therefore AB is parallel to FG . And AB is at right angles to the plane CK ; therefore FG is also at right angles to the ...
... consequently it is perpendicular to CE . Where- fore ABF is a right angle ; but GFB is likewise a right angle ; therefore AB is parallel to FG . And AB is at right angles to the plane CK ; therefore FG is also at right angles to the ...
Página 29
... ; I , K , L , and M , their respective altitudes ; and consequently the rectangles AE , BF , C.G , and DH , their bases . Then ( Pl . Ge . VI . 23 , Cor . 1 ) AE : B · FC⋅G : D H. But C ( II . 11 ) P : Q = ( SECOND BOOK . 29.
... ; I , K , L , and M , their respective altitudes ; and consequently the rectangles AE , BF , C.G , and DH , their bases . Then ( Pl . Ge . VI . 23 , Cor . 1 ) AE : B · FC⋅G : D H. But C ( II . 11 ) P : Q = ( SECOND BOOK . 29.
Página 33
... consequently similar ; and the same is true of the triangles NOP , FGH . - Now , since the straight lines ARQ , AKB , meet the pa- rallel planes BDC and KML , they are cut by them propor- tionally ( I. 16 ) , or QR : RA = BK : KA ; and ...
... consequently similar ; and the same is true of the triangles NOP , FGH . - Now , since the straight lines ARQ , AKB , meet the pa- rallel planes BDC and KML , they are cut by them propor- tionally ( I. 16 ) , or QR : RA = BK : KA ; and ...
Página 49
... consequently right angles . D E G But , since the arc AB is equal to the arc AC , the angle ADB is equal to the angle ADC . Therefore the triangles ADE , ADF , have the angles EDA , FDA , equal , as also the angles AED , AFD , which are ...
... consequently right angles . D E G But , since the arc AB is equal to the arc AC , the angle ADB is equal to the angle ADC . Therefore the triangles ADE , ADF , have the angles EDA , FDA , equal , as also the angles AED , AFD , which are ...
Otras ediciones - Ver todas
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... A. Bell Vista completa - 1837 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Sin vista previa disponible - 2018 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Sin vista previa disponible - 2015 |
Términos y frases comunes
absciss altitude angle ABC assymptotes base centre CG² circumference common section cone Conic Sections conic surface conjugate axis conjugate diameters cord cosine cotangent dicular directrix distance draw EK KF ellipse equal Pl foci focus given angle given point greater Hence hyperbola hypotenuse inclination intercepted intersection Let ABC line be drawn line of common ordinate parabola parallel planes parallelogram pendicular perpen perpendicular perspective plane passing point of contact pole primitive prism projection pyramid ABCD quadrant radius ratio rectangle right angles right-angled spherical triangles segments semi-ordinate semicircle sides similar triangles sine small circle solid angle solid KQ solid less solid parallelopipeds sphere spherical angle spherical triangle square subcontrary surface tangent THEOREM transverse axis vertex vertical wherefore
Pasajes populares
Página 52 - 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.
Página 17 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 27 - LR, the base of which is the parallelogram LQ, and of which LM is one of its insisting straight lines : therefore, because the parallelogram AB is equal to CD, as the base AB is to the base LQ, so is (7.
Página 19 - DAB, which contain the solid angle at A, are less than four right angles. Next, let the solid angle at A be contained by any number of plane angles BAC, CAD, DAE, EAF, FAB. These shall together be less than four right angles.
Página 29 - FC, as the solid HD to the solid DC. But the base HF is equal to the base AE, and the solid GK to the solid AB ; therefore, as the base AE to the base CF, so is the solid AB to the solid CD.
Página 55 - EM (2.) are ^quadrants, and FL, EM together, that is, FE and ML together, are equal to a semicircle. But since A is the pole of ML, ML is the measure of the angle BAC (3.), consequently FE is the supplement of the measure of the angle BAC.
Página 21 - And AB is parallel to CD ; therefore AC is a parallelogram. In like manner, it may be proved, that each of the figures CE, FG, GB, BF, AE is a parallelogram: Join AH, DF; and...
Página 7 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane.
Página 11 - CA is at right angles to the given plane, it makes right angles with every straight line meeting it in that plane. But DAE, which is in that plane, meets CA : therefore CAE is a right angle. For the same reason BAE is a right angle. Wherefore the angle CAE is equal to the angle BAE ; and they are in one plane, which is impossible. Also, from a point above a plane, there can be but one perpendicular to that plane ; for if there could be two, they would be parallel (6.
Página 3 - The inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the point in which...