Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 42
... Schol . 29. I. e 29 def . a с For fince the Ang . A + D2 right Ang . the Lines AB , DC fhall be parallel . But they are alfo equal . Whence AD , BC are like- wife equal and parallel ; therefore the Figure AC is a Parallelogram , having ...
... Schol . 29. I. e 29 def . a с For fince the Ang . A + D2 right Ang . the Lines AB , DC fhall be parallel . But they are alfo equal . Whence AD , BC are like- wife equal and parallel ; therefore the Figure AC is a Parallelogram , having ...
Página 72
... Schol . 48 . 1 . € 6. ax . f 15.def . 1 . € 20. I. h 24. I. PRO P. XIV . G In a Circle EABC equal right Lines AC , BD , are e- qually diftant from the Center E and thofe right Lines AC , BD that are equally diftant from the Center are ...
... Schol . 48 . 1 . € 6. ax . f 15.def . 1 . € 20. I. h 24. I. PRO P. XIV . G In a Circle EABC equal right Lines AC , BD , are e- qually diftant from the Center E and thofe right Lines AC , BD that are equally diftant from the Center are ...
Página 86
... the right Lines cut each other in the Centre , the thing is clear . Cafe 2. If one of them , as AB , paffes thro ' the Centre F , and bifects the other CD , draw FD . Then 2 a = a 5.2 . Schol . Then the 86 EUCLID'S Elements .
... the right Lines cut each other in the Centre , the thing is clear . Cafe 2. If one of them , as AB , paffes thro ' the Centre F , and bifects the other CD , draw FD . Then 2 a = a 5.2 . Schol . Then the 86 EUCLID'S Elements .
Página 87
Euclid. 2 a = a 5.2 . Schol . Then the Rectang . AEB + FE FB2 FD = ED + FE2 = CED + FE . There- 48. 1 . fore the Rectang . AEB = CED . Q.E.D. 47. 1 . e 3. If one of them , as AB , be a Diameter , cut- ting the other CD unequally , and ...
Euclid. 2 a = a 5.2 . Schol . Then the Rectang . AEB + FE FB2 FD = ED + FE2 = CED + FE . There- 48. 1 . fore the Rectang . AEB = CED . Q.E.D. 47. 1 . e 3. If one of them , as AB , be a Diameter , cut- ting the other CD unequally , and ...
Página 90
Euclid. a 17.3 . C b Hyp . 36.3 . Lax . & Schol . 48 . I. € 8 , I. f 18. 3 : 8. I. 4 DB the infident Line ; the faid Line DB ball touch the Circle . 2 From D draw the Tangent DF ; and draw ED , EB , EF from the Centre E. Because DB = ADC ...
Euclid. a 17.3 . C b Hyp . 36.3 . Lax . & Schol . 48 . I. € 8 , I. f 18. 3 : 8. I. 4 DB the infident Line ; the faid Line DB ball touch the Circle . 2 From D draw the Tangent DF ; and draw ED , EB , EF from the Centre E. Because DB = ADC ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.