Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Seite 3
... faid to be fo much the lefs , the nearer the Lines that make it are to one ano- B A A ther . Take two Lines AB , BC , touching one another in B : then if you conceive these two Lines to open like the Legs of a Pair of Com- paffes , fo ...
... faid to be fo much the lefs , the nearer the Lines that make it are to one ano- B A A ther . Take two Lines AB , BC , touching one another in B : then if you conceive these two Lines to open like the Legs of a Pair of Com- paffes , fo ...
Seite 9
... faid before . Poftulates or Petitions . 1. Grant that a right Line may be drawn from any Point to any other Point . 2. That a finite right Line may be drawn out at pleasure . 3. That a Circle may be defcribed about any Centre with any ...
... faid before . Poftulates or Petitions . 1. Grant that a right Line may be drawn from any Point to any other Point . 2. That a finite right Line may be drawn out at pleasure . 3. That a Circle may be defcribed about any Centre with any ...
Seite 20
... any ftrait Line E ( AB ) Jo that the An- gles ( ABC , ABD ) on each fide AB be equal to two right Angles : the faid Lines CB , BD , lie both in C B D the the fame Direction , that is , they are one 20 EUCLID'S Elements .
... any ftrait Line E ( AB ) Jo that the An- gles ( ABC , ABD ) on each fide AB be equal to two right Angles : the faid Lines CB , BD , lie both in C B D the the fame Direction , that is , they are one 20 EUCLID'S Elements .
Seite 21
... faid Lines EA , AF , lie both in the fame strait Line . For the Angle D + A e 3 ax . two right Angles , f 13. 1 . = B + A : therefore EA , AF , lie both in the g 14. 1 . fame ftrait Line . Q. E. D. C SCHOLIUM II . E A B D If four ftrait ...
... faid Lines EA , AF , lie both in the fame strait Line . For the Angle D + A e 3 ax . two right Angles , f 13. 1 . = B + A : therefore EA , AF , lie both in the g 14. 1 . fame ftrait Line . Q. E. D. C SCHOLIUM II . E A B D If four ftrait ...
Seite 23
... faid to be a Perpendicular ; then in the Tri- angle AEC , the Angle AEC + ACE fhall be two right Angles , which is abfurd . 3. All the Angles of an equilateral Triangle , and those two of an Ifofceles one that are above the Bafe , are ...
... faid to be a Perpendicular ; then in the Tri- angle AEC , the Angle AEC + ACE fhall be two right Angles , which is abfurd . 3. All the Angles of an equilateral Triangle , and those two of an Ifofceles one that are above the Bafe , are ...
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.