Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Seite 9
... third Thing , are alfo equal the one to the other . As , if ABC ; then is A = C : or therefore all the Quantities A , B , C , are equal the one to the other . Note . When you find several Quantities con- nected together after this ...
... third Thing , are alfo equal the one to the other . As , if ABC ; then is A = C : or therefore all the Quantities A , B , C , are equal the one to the other . Note . When you find several Quantities con- nected together after this ...
Seite 10
... third thing , or of equal things , are equal one to the other . Understand the fame of things that are the triple , quadruple , & c . of the fame thing . As if A 2 B , and C 2 B : then fhall AC . = 7. Things which are the half of the ...
... third thing , or of equal things , are equal one to the other . Understand the fame of things that are the triple , quadruple , & c . of the fame thing . As if A 2 B , and C 2 B : then fhall AC . = 7. Things which are the half of the ...
Seite 25
... third ; because any two Sides of a Triangle taken together , are longer than the third . In the Infinite Line DE take orderly a DF , a 3. 1 . FG , GH , equal to the given Lines A , B , C ; then if with the Centers F and G , and the Di ...
... third ; because any two Sides of a Triangle taken together , are longer than the third . In the Infinite Line DE take orderly a DF , a 3. 1 . FG , GH , equal to the given Lines A , B , C ; then if with the Centers F and G , and the Di ...
Seite 43
... third Side CE , from B to E , and join EX , and then shall EX ' = EB ' ( CE ' ) + BX ' ( AC ' ) = CE2 + AB + BC . Q. E. F. F A E h B fhall ACAB2 + BC2 . PROB . a 47. I. 3 ax . A B the leffer Book I. EUCLID's Elements . 43.
... third Side CE , from B to E , and join EX , and then shall EX ' = EB ' ( CE ' ) + BX ' ( AC ' ) = CE2 + AB + BC . Q. E. F. F A E h B fhall ACAB2 + BC2 . PROB . a 47. I. 3 ax . A B the leffer Book I. EUCLID's Elements . 43.
Seite 44
... third Side . Let AC , AB , be the Sides containing the right Angle ; one of which let be 8 , and the other 6. There- C fore fince AC + AB 2 = 64 + 36 = 100 = BC2 . Therefore fhall BC = fquare Root of 100 = IO . Again , let AB , BC be ...
... third Side . Let AC , AB , be the Sides containing the right Angle ; one of which let be 8 , and the other 6. There- C fore fince AC + AB 2 = 64 + 36 = 100 = BC2 . Therefore fhall BC = fquare Root of 100 = IO . Again , let AB , BC be ...
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.