c.  1  def.  6
T.  10.  def.  11
v.  cas.  1.

EVCLIDIS  ELEMENT.
338
Cas.  1.  Sint  ina
BO
L
sistentes  lineae  A
G,  BE,  HI,  KL
CM,  DE,  NO,  PG
o
ad  rectos  angulose
basibus  AE,  CF,  &  sit  ang.  PFN—HEK
NF  =  KE,  &  FP=  EH.  Erit  ergo  Pgr
CE=  &  O°  Pgro.  AE.  Eadem  ratione  quia
altitudines  NO,  KL  aequales,  &  ang.  ONF
ONC,  LKE,  LKA  recti  sunt:  erit  Pgr.  ND
=  &  (  ipsi  KB,  &  Pgr.  CO.=  &  GALI
Quare  &  reliqua  Pgra  reliquis  aequalia  &  similia ¬
  erunt,  &  ergo  Ppd.  CD  —  ipsi  ABQ. ¬
  E.  D.
M
71
E
R
XS
Cas.  2.  Sint  iterum  insistentes  perpendiculares, ¬
  sed  ang.  PFN  non  =  HEK.  Produc.
NF  in  Q,  &  fac  ang.  QFR  —  HEK,  &  FO
—  HE,  &  FR  —  EK,  &  comple  Pgr.  QR  ach
solidum  TR.  Ergo  erit  Ppd.  TR
Ppdob
AB.  Produc  PF,  SR,  quae  conueniant  in  V,  &  &
per  Qduc  ipsi  PV  parallelam  QX,  quam  producb
donec  productae  CP  occurrat  in  Y,  &  comple ¬
  Ppda  TV,  TP,  quorum  bases  sunt  Pgra.
V