Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Σελίδα 7
... felves , nor the Angles right ones ; as CLMH . N 33. All other Qua- drilateral Figures be- fides thefe , are cal- led Trapeziums ; as GNDH . G H B 4 34 . A- B- 34. Parallel , or E- quidiftant right Lines Book I. 7 Definitions .
... felves , nor the Angles right ones ; as CLMH . N 33. All other Qua- drilateral Figures be- fides thefe , are cal- led Trapeziums ; as GNDH . G H B 4 34 . A- B- 34. Parallel , or E- quidiftant right Lines Book I. 7 Definitions .
Σελίδα 8
... parallel or equi- G M diftant ; asGLHM . A E B H 36. In a Pa- rallelogram A B CD , when a Diameter A C , and two Lines F C EF , HI , paral- lel to the Sides , cutting the Dia- D meter in one or the fame Point G , are drawn fo , that the ...
... parallel or equi- G M diftant ; asGLHM . A E B H 36. In a Pa- rallelogram A B CD , when a Diameter A C , and two Lines F C EF , HI , paral- lel to the Sides , cutting the Dia- D meter in one or the fame Point G , are drawn fo , that the ...
Σελίδα 28
... parallel , pro- 116. 1. duce them till they meet , fuppofe in G : Then the outward Angle AEF will be greater than the inward Angle DFE , to which it was equal by the Hypothefis : Which is abfurd . PROP . PROP . XXVIII . E A- C H F If 28 ...
... parallel , pro- 116. 1. duce them till they meet , fuppofe in G : Then the outward Angle AEF will be greater than the inward Angle DFE , to which it was equal by the Hypothefis : Which is abfurd . PROP . PROP . XXVIII . E A- C H F If 28 ...
Σελίδα 29
... parallel . = Hyp . 1. Becaufe by the Hypothefis the Ang . AGE CHG , therefore the alternate Angles BGH , CHG are equal : and confequently ABa 15. 1 . and CD are parallel . b a 111 b 27. I. Hyp . 2. Becaufe by the Hypothefis the Ang ...
... parallel . = Hyp . 1. Becaufe by the Hypothefis the Ang . AGE CHG , therefore the alternate Angles BGH , CHG are equal : and confequently ABa 15. 1 . and CD are parallel . b a 111 b 27. I. Hyp . 2. Becaufe by the Hypothefis the Ang ...
Σελίδα 30
... parallel to one A B and the fame right H E -F Line ( EF ) are also parallel the one to the C D other . Let the Line GI cut the three given Lines any how ; then because AB , EF are parallel , the Angle c 29.1 . AGI will be EHI : alfo ...
... parallel to one A B and the fame right H E -F Line ( EF ) are also parallel the one to the C D other . Let the Line GI cut the three given Lines any how ; then because AB , EF are parallel , the Angle c 29.1 . AGI will be EHI : alfo ...
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.