Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
Im Buch
Ergebnisse 1-5 von 14
Seite 98
... EFGH infcrib'd in the fame . G D For the Rectang . HB = 2HEF and HD = 2HGF , by 41. I. PRO P. VIII . Probl . 8 . A H D E B Circle To infcribe a IEFGH in a given Square ABCD . Bife & t the Sides of the G Square in the Points H , E , F ...
... EFGH infcrib'd in the fame . G D For the Rectang . HB = 2HEF and HD = 2HGF , by 41. I. PRO P. VIII . Probl . 8 . A H D E B Circle To infcribe a IEFGH in a given Square ABCD . Bife & t the Sides of the G Square in the Points H , E , F ...
Seite 184
... Ppp . FINM ; it FINM ( ABCD ) : Q. E. D. PROP . XXXIII . Similar folid Parallelepipedons ABCD , EFGH , are to one another in the triplicate proportion of their Homologous Sides AI , EK . Con- S G R. Q H F E K A D 184 EUCLID'S Elements .
... Ppp . FINM ; it FINM ( ABCD ) : Q. E. D. PROP . XXXIII . Similar folid Parallelepipedons ABCD , EFGH , are to one another in the triplicate proportion of their Homologous Sides AI , EK . Con- S G R. Q H F E K A D 184 EUCLID'S Elements .
Seite 185
... ( EFGH ) . Therefore the Ra- f 10 def . 5 . tio of ABCD to EFGH is triplicate of the Ratio of ABCD , to DLQY , or of AI to EK . 81. 6 Q : E. D. CORO L. f Hence if there be four right Lines continu- ally Proportional , as the first is to ...
... ( EFGH ) . Therefore the Ra- f 10 def . 5 . tio of ABCD to EFGH is triplicate of the Ratio of ABCD , to DLQY , or of AI to EK . 81. 6 Q : E. D. CORO L. f Hence if there be four right Lines continu- ally Proportional , as the first is to ...
Seite 196
... I , Then I fay that I Cir . EFN . For firft , if poffible , let I be less than the Circle EFN , and let K be the Excefs or Dif- ference . Infcribe the Square EFGH in the C a d e 41. 1 . Circle EFN , Circle 196 EUCLID'S Elements . b 6.6. ...
... I , Then I fay that I Cir . EFN . For firft , if poffible , let I be less than the Circle EFN , and let K be the Excefs or Dif- ference . Infcribe the Square EFGH in the C a d e 41. 1 . Circle EFN , Circle 196 EUCLID'S Elements . b 6.6. ...
Seite 197
... EFGH be taken from the Circle EFN , and the Triangles from the other Segments , and this be done continually , there willat laft remain fome Magnitude lefs 1. 10 . than K. Let us have gone fo far , viz . to the Seg- ments EL , LF , FM ...
... EFGH be taken from the Circle EFN , and the Triangles from the other Segments , and this be done continually , there willat laft remain fome Magnitude lefs 1. 10 . than K. Let us have gone fo far , viz . to the Seg- ments EL , LF , FM ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.