Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Σελίδα 8
... Whole is grea- ter than its Part , & c . A Theorem is fomething propofed , the Truth of which is to be made appear ( which is called demonftrating it ) fo evidently , that all fcruple con- concerning the fame may vanifh ; as that the ...
... Whole is grea- ter than its Part , & c . A Theorem is fomething propofed , the Truth of which is to be made appear ( which is called demonftrating it ) fo evidently , that all fcruple con- concerning the fame may vanifh ; as that the ...
Σελίδα 10
... equal , or the fame Space . 9. Every Whole is greater than its Part . 10. Two right Lines cannot have one and the fame Segment ( or Part ) common to them both . 11. Two 11. Two right Lines meeting in the fame Point , ΤΟ EUCLID'S Elements .
... equal , or the fame Space . 9. Every Whole is greater than its Part . 10. Two right Lines cannot have one and the fame Segment ( or Part ) common to them both . 11. Two 11. Two right Lines meeting in the fame Point , ΤΟ EUCLID'S Elements .
Σελίδα 11
... whole fhall be equal to the excess of the unequal things before the Ad- dition . If A = B , and CD ; then shall A + C - B - D be A - B . 17. If from equal things unequal things be taken away , the excefs of the ' remainders fhall be ...
... whole fhall be equal to the excess of the unequal things before the Ad- dition . If A = B , and CD ; then shall A + C - B - D be A - B . 17. If from equal things unequal things be taken away , the excefs of the ' remainders fhall be ...
Σελίδα 12
Euclid. 19. Every Whole is equal to all its Parts ta- ken together . 20. If one whole thing be the double of an- other , and that which is taken away from the firft , the double of that which is taken away from the fecond , the remainder ...
Euclid. 19. Every Whole is equal to all its Parts ta- ken together . 20. If one whole thing be the double of an- other , and that which is taken away from the firft , the double of that which is taken away from the fecond , the remainder ...
Σελίδα 16
... Whole : which is fabfurd . = с CORO L. Hence every equiangular Triangle is alfo e- quilateral . PROP . VII . If from the Extremes ( A , B ) of a right Line , two right Lines ( AC , BC ) be drawn to any Point C ; you · cannot draw two ...
... Whole : which is fabfurd . = с CORO L. Hence every equiangular Triangle is alfo e- quilateral . PROP . VII . If from the Extremes ( A , B ) of a right Line , two right Lines ( AC , BC ) be drawn to any Point C ; you · cannot draw two ...
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.