Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Σελίδα 163
... Cone is a rectangular Cone ; but if it be lefs , it is an obtuse - angled Cone ; if greater , an acute - angled Cone : XIX . The Axis of a Cone is that fixed Right Line about which the Triangle is moved . M 2 XX . XX . The Bafe of a ...
... Cone is a rectangular Cone ; but if it be lefs , it is an obtuse - angled Cone ; if greater , an acute - angled Cone : XIX . The Axis of a Cone is that fixed Right Line about which the Triangle is moved . M 2 XX . XX . The Bafe of a ...
Σελίδα 164
Euclid. XX . The Bafe of a Cone is the Circle defcribed by the Right Line moved about . 1 XXI . A Cylinder is a ... Cones and Cylinders are fuch , whofe Axes and Diameters of their Bafes are pro- portional . XXV . A Cube is a folid Figure ...
Euclid. XX . The Bafe of a Cone is the Circle defcribed by the Right Line moved about . 1 XXI . A Cylinder is a ... Cones and Cylinders are fuch , whofe Axes and Diameters of their Bafes are pro- portional . XXV . A Cube is a folid Figure ...
Σελίδα 206
... Cone by the Magnitude E. Now a Prism standing upon the Square ABCD infcrib'd within the Circle , is the one half of ... Cones 3 Cy $ 206 EUCLID'S Elements . a Cor. 1. ...
... Cone by the Magnitude E. Now a Prism standing upon the Square ABCD infcrib'd within the Circle , is the one half of ... Cones 3 Cy $ 206 EUCLID'S Elements . a Cor. 1. ...
Σελίδα 207
... Cone . he right Lines VK , CK , VI , PR , QL , RL . Because the herefore VI : IK :: GL : Cylinders and Cones es VIK , GLM are Same Altitude , are to he Triangles VIK , Whence VC : VI Let the Circ . ABCI : GL : GM . ABCDK : Solid N. IK ...
... Cone . he right Lines VK , CK , VI , PR , QL , RL . Because the herefore VI : IK :: GL : Cylinders and Cones es VIK , GLM are Same Altitude , are to he Triangles VIK , Whence VC : VI Let the Circ . ABCI : GL : GM . ABCDK : Solid N. IK ...
Σελίδα 208
... Cone by th : ABCD . Noh is abfurd , from uponftrated in the for- infe Then Cinclude that ABCD : hal Cone EFGHM . ing upon the Square circu Circle , and the Cylinder c Therefore , a Prifm ftandi O L. ABCD does exceed the solidity of any ...
... Cone by th : ABCD . Noh is abfurd , from uponftrated in the for- infe Then Cinclude that ABCD : hal Cone EFGHM . ing upon the Square circu Circle , and the Cylinder c Therefore , a Prifm ftandi O L. ABCD does exceed the solidity of any ...
Συχνά εμφανιζόμενοι όροι και φράσεις
9 ax ABCD abfurd alfo alſo Altitude Angle ABC Bafe BC Baſe becauſe bifect Center Circ Cone confequently conft COROL Cylinder defcribed demonftrated Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples EUCLID's ELEMENTS faid fame Multiple fecond fhall fimilar fince firft folid fome fore four right ftanding given right Line gles Gnomon greater Hence infcribe leffer lefs likewife Line CD Magnitudes manifeft manner Number oppofite Paral parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular poffible Point Polyhedron Prifms Probl PROP Propofition Pyramids Ratio Rectangle right Angles right Line AB right Line AC right-lined Figure SCHOL SCHOLIU Segment ſhall Side BC Sphere Square thefe thofe thro tiple Triangle ABC Whence whofe whole
Δημοφιλή αποσπάσματα
Σελίδα 31 - 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 145 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Σελίδα 33 - ABD, is equal* to two right angles, «13. 1. therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are sides of the figure; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles; therefore all the exterior angles are equal to four right angles.
Σελίδα 27 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Σελίδα 31 - The three angles of any triangle taken together are equal to the three angles of any other triangle taken together. From whence it follows, 2.
Σελίδα 11 - That a straight line may be drawn from any point to any other point. 2. That a straight line may be produced to any length in a straight line.