Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 62
... Arch AB of a Circle . 7. An Ang . ( ABC ) is faid to be in a Segment ( ABC ) when fome Point B is taken , in the Cir- cumference thereof , and from it right Lines ( AB , CB ) are drawn to the Extremes of the right Line AC , which is the ...
... Arch AB of a Circle . 7. An Ang . ( ABC ) is faid to be in a Segment ( ABC ) when fome Point B is taken , in the Cir- cumference thereof , and from it right Lines ( AB , CB ) are drawn to the Extremes of the right Line AC , which is the ...
Página 75
... Circle DABC , the Ang . BDC at the Centre is the double of the Angle BAC at the Peri- phery , the fame Arch BC being C the Bafe of the Angles . A E D 22 B B A Draw 9. ax . a 32. I. 5. I. 2. ax . d 20.ax. Book III . 75 EUCLID'S Elements .
... Circle DABC , the Ang . BDC at the Centre is the double of the Angle BAC at the Peri- phery , the fame Arch BC being C the Bafe of the Angles . A E D 22 B B A Draw 9. ax . a 32. I. 5. I. 2. ax . d 20.ax. Book III . 75 EUCLID'S Elements .
Página 80
... Arch AD be equal to the Arch DC ; then hall AD be parallel to BC . For drawing AC , and then the Ang . ACB fhall be a Whence by Prop . 27. L. PROP . XXVII . CAD . AD is In equal Circles GABC , HDEF , the Angles ftanding upon egual Parts ...
... Arch AD be equal to the Arch DC ; then hall AD be parallel to BC . For drawing AC , and then the Ang . ACB fhall be a Whence by Prop . 27. L. PROP . XXVII . CAD . AD is In equal Circles GABC , HDEF , the Angles ftanding upon egual Parts ...
Página 82
... Arch AIC DKF , and fo the remaining Arch ABC DEF . Q.E.D. = But if the intended Line AC be or than DF ; then in like manner will the Arch AIC be or than DKF . PROP . XXIX . In equal Circles GABC , HDEF , equal right Lines AC , DF ...
... Arch AIC DKF , and fo the remaining Arch ABC DEF . Q.E.D. = But if the intended Line AC be or than DF ; then in like manner will the Arch AIC be or than DKF . PROP . XXIX . In equal Circles GABC , HDEF , equal right Lines AC , DF ...
Página 83
Euclid. meeting the Arch in B ; and it fhall bifect the fame . - ba b For join AB and CB . Then the Side DB is common and AD DC , and the Ang . ADB a Conft . CDB . Therefore AB BC ; whence the 12. ax . BC . Q. E. F. Arch AB = PROP . XXXI ...
Euclid. meeting the Arch in B ; and it fhall bifect the fame . - ba b For join AB and CB . Then the Side DB is common and AD DC , and the Ang . ADB a Conft . CDB . Therefore AB BC ; whence the 12. ax . BC . Q. E. F. Arch AB = PROP . XXXI ...
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.