Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
Inni boken
Resultat 1-5 av 34
Side 4
... each of thofe equal Angles is call'd a Right Angle ; B and the right Line CG thus ftanding , is called a Perpendicular to the Line AB , upon which it ftands . 11. An B. A V D 11. An Obtufe An- gle is 4 EUCLID'S Elements .
... each of thofe equal Angles is call'd a Right Angle ; B and the right Line CG thus ftanding , is called a Perpendicular to the Line AB , upon which it ftands . 11. An B. A V D 11. An Obtufe An- gle is 4 EUCLID'S Elements .
Side 19
... Perpendicular required . a I. I. c conftr . d 4.1 . e 3.1 . f I. I. For CECD , and CF is common , and DF = EF ( by Conft . ) whence the Triangles DFC , EFC are mutually equilateral ; therefore & the SS . 1 . Angle DCF = ECF ; whence FC ...
... Perpendicular required . a I. I. c conftr . d 4.1 . e 3.1 . f I. I. For CECD , and CF is common , and DF = EF ( by Conft . ) whence the Triangles DFC , EFC are mutually equilateral ; therefore & the SS . 1 . Angle DCF = ECF ; whence FC ...
Side 20
... Perpendicular required . Draw the Lines CE , CF ; then the Triangles EGC , FGC are mutually equilateral : There- fore the Angles EGC , FGC are equal , and by e 10 def . confequence right ones : wherefore GC is a Perpendicular . QE.F d 8 ...
... Perpendicular required . Draw the Lines CE , CF ; then the Triangles EGC , FGC are mutually equilateral : There- fore the Angles EGC , FGC are equal , and by e 10 def . confequence right ones : wherefore GC is a Perpendicular . QE.F d 8 ...
Side 23
... perpendicular Line AD let fall from any Point ( A ) thereof to that other Line CD , will fall next to the acute Angle AED . For if AC drawn towards the obtufe Angle be faid to be a Perpendicular ; then in the Tri- angle AEC , the Angle ...
... perpendicular Line AD let fall from any Point ( A ) thereof to that other Line CD , will fall next to the acute Angle AED . For if AC drawn towards the obtufe Angle be faid to be a Perpendicular ; then in the Tri- angle AEC , the Angle ...
Side 48
... perpendicular to AB , and through F draw the infinite Line FG perpendicular to AF ; and from D , E , B raife the Perpendicu- lars DH , EI , BG . Now AG fhall be the Rec- 19 ax . 1. tangle under AF , AB ; and it is equal to the ...
... perpendicular to AB , and through F draw the infinite Line FG perpendicular to AF ; and from D , E , B raife the Perpendicu- lars DH , EI , BG . Now AG fhall be the Rec- 19 ax . 1. tangle under AF , AB ; and it is equal to the ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.