Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 47
... comprehending a right Angle . D 2. In every Parallelogramick Space FHIK , each of thofe Parallelograms which are about its Diameter , with the two Complements , is call'd K M I A EF call'd a Gnomon ; as ( 47 ) EUCLID's ...
... comprehending a right Angle . D 2. In every Parallelogramick Space FHIK , each of thofe Parallelograms which are about its Diameter , with the two Complements , is call'd K M I A EF call'd a Gnomon ; as ( 47 ) EUCLID's ...
Página 48
... Gnomon . Alfo the G H Pgr.FE | BI | EM , that is , GKA is a Gnomon . 3. A Figure is faid to be conftructed , when Lines drawn parallel to the Sides cutting the Diameter in one Point , make two Parallelograms about the Dia- meter ...
... Gnomon . Alfo the G H Pgr.FE | BI | EM , that is , GKA is a Gnomon . 3. A Figure is faid to be conftructed , when Lines drawn parallel to the Sides cutting the Diameter in one Point , make two Parallelograms about the Dia- meter ...
Página 51
... Gnomon NMX + LG = AD x DB + CD ' . But the Gnomon NMX + LG whole Square CEFB = CB2 . Therefore AD x DB + CD ' CB ' . Q. E D. cor . 4. 2 . PROP . VI . E G F K L H A B E 2 If any right . Line AB be bi- fected in the Point C , and a- ny ...
... Gnomon NMX + LG = AD x DB + CD ' . But the Gnomon NMX + LG whole Square CEFB = CB2 . Therefore AD x DB + CD ' CB ' . Q. E D. cor . 4. 2 . PROP . VI . E G F K L H A B E 2 If any right . Line AB be bi- fected in the Point C , and a- ny ...
Página 52
... Gnomon NXO . But AM ADX DB ( fince DM d = DB ) therefore the Gnomon NXỞ = AD × DB . Again , adding LGCB ' , which is com- mon ; and then AD × DB + BC2 = Gnomon NXO + LG whole Square CF = CD ' · Q. E. D. = 3 PROP . VII ...
... Gnomon NXO . But AM ADX DB ( fince DM d = DB ) therefore the Gnomon NXỞ = AD × DB . Again , adding LGCB ' , which is com- mon ; and then AD × DB + BC2 = Gnomon NXO + LG whole Square CF = CD ' · Q. E. D. = 3 PROP . VII ...
Página 54
... Gnomon PY + AC2 = = AD2 . QE . D. E C PROP . IX . If a right Line AB be cut into two equal parts in C , and two un- equal ones in D ; then the Squares of the un- equal Parts AD , DB B together , are the Dou- ble of the Square of the ...
... Gnomon PY + AC2 = = AD2 . QE . D. E C PROP . IX . If a right Line AB be cut into two equal parts in C , and two un- equal ones in D ; then the Squares of the un- equal Parts AD , DB B together , are the Dou- ble of the Square of the ...
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.