Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Αποτελέσματα 1 - 5 από τα 61.
Σελίδα
... fince in Latin by our famous Dr. Barrow , viz . the first Six , Eleventh and Twelfth ; which are a fufficient Foundation for all the other useful Parts of Mathematicks ; A 2 the the others being not near fo necessary to be known ( iii )
... fince in Latin by our famous Dr. Barrow , viz . the first Six , Eleventh and Twelfth ; which are a fufficient Foundation for all the other useful Parts of Mathematicks ; A 2 the the others being not near fo necessary to be known ( iii )
Σελίδα 17
... fince BD BC , then fhall the c fup . - = с Angle FDC be ECD . Therefore the An - d 9 ax . gled FDCACD ; that is , the Angle & FDC ADC : which is abfurd . Cafe 3. If the Point D falls without the Tri- angle ACB , then join CD . e Again ...
... fince BD BC , then fhall the c fup . - = с Angle FDC be ECD . Therefore the An - d 9 ax . gled FDCACD ; that is , the Angle & FDC ADC : which is abfurd . Cafe 3. If the Point D falls without the Tri- angle ACB , then join CD . e Again ...
Σελίδα 18
... fince . AB ab , and AC ac , the Point A will fall on a , ( for it cannot fall on any other Point , by the laft Propofition ; ) and fo the Sides of the An- gles A and a do coincided : wherefore those Angles are equal . Q. E. D. ...
... fince . AB ab , and AC ac , the Point A will fall on a , ( for it cannot fall on any other Point , by the laft Propofition ; ) and fo the Sides of the An- gles A and a do coincided : wherefore those Angles are equal . Q. E. D. ...
Σελίδα 26
... fince ac ag , therefore is the g Angle acg hagc . And fo the Angle acg hbgc , and confequently the Angle begh bgc . Therefore bg ( BC ) i 10. J Q. E. D. C bc . Cafe Cafe 2. When the Bafe bg coincides with bc , 27 EUCLID'S Elements .
... fince ac ag , therefore is the g Angle acg hagc . And fo the Angle acg hbgc , and confequently the Angle begh bgc . Therefore bg ( BC ) i 10. J Q. E. D. C bc . Cafe Cafe 2. When the Bafe bg coincides with bc , 27 EUCLID'S Elements .
Σελίδα 30
... fince A is a right Angle , B must be balfo a right Angle . By the fame Argument C and D are right Angles . PROP . XXX . Right Lines ( AB , G CD ) parallel to one A B and the fame right H E -F Line ( EF ) are also parallel the one to the ...
... fince A is a right Angle , B must be balfo a right Angle . By the fame Argument C and D are right Angles . PROP . XXX . Right Lines ( AB , G CD ) parallel to one A B and the fame right H E -F Line ( EF ) are also parallel the one to the ...
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.