Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
Inni boken
Resultat 1-5 av 15
Side 62
... AC , BC drawn from the Center C , and the Cir- cumference AB between them . 10. Similar Segments ABC , DEF of a Circle , are those which include equal Angles ( ABC , DEF ) or B E A C D F or whereof the Angles 62 EUCLID's Elements .
... AC , BC drawn from the Center C , and the Cir- cumference AB between them . 10. Similar Segments ABC , DEF of a Circle , are those which include equal Angles ( ABC , DEF ) or B E A C D F or whereof the Angles 62 EUCLID's Elements .
Side 78
... Similar Segments ABC , DEF of Circles , be- ing upon equal right Lines AC , DF , are equal to each other . B E A C D E E B B D A FA C D 2 a 23. 3 . b 10. 3 . € 8. ax . + For if the Bafe AC be laid upon the Base DF , they will coincide ...
... Similar Segments ABC , DEF of Circles , be- ing upon equal right Lines AC , DF , are equal to each other . B E A C D E E B B D A FA C D 2 a 23. 3 . b 10. 3 . € 8. ax . + For if the Bafe AC be laid upon the Base DF , they will coincide ...
Side 146
... Similar Trian- gles ABC , DFE , D are in the Dupli- cate Proportion of their Homologous Sides BC , FE . Make BC : તા EF :: EF : BG , E and draw AG . cor . 4. 6 . & conft . 15.6 . 11 I. 6 . 1 10. def.5 . * 11. 5 . becaufe AB : DF ...
... Similar Trian- gles ABC , DFE , D are in the Dupli- cate Proportion of their Homologous Sides BC , FE . Make BC : તા EF :: EF : BG , E and draw AG . cor . 4. 6 . & conft . 15.6 . 11 I. 6 . 1 10. def.5 . * 11. 5 . becaufe AB : DF ...
Side 147
Euclid. PROP . XX . Similar Polygons ABCDE , FGHIK are divided into fimilar Triangles ABC , FGH ; and ACD , FHI and ADE , FIK , equal in Number and Homo- logous to the holes ( ABC : FGH :: ABCDE : FGHIK :: ACD : FHI :: ADE : FIK ) and ...
Euclid. PROP . XX . Similar Polygons ABCDE , FGHIK are divided into fimilar Triangles ABC , FGH ; and ACD , FHI and ADE , FIK , equal in Number and Homo- logous to the holes ( ABC : FGH :: ABCDE : FGHIK :: ACD : FHI :: ADE : FIK ) and ...
Side 162
... Planes are fuch , which being pro- duced , never meet . IX . Similar folid Figures are fuch that are con tained under equal Numbers of fimilar Planes . X. Equal and fimilar folid Figures , are thofe that 162 EUCLID'S Elements :
... Planes are fuch , which being pro- duced , never meet . IX . Similar folid Figures are fuch that are con tained under equal Numbers of fimilar Planes . X. Equal and fimilar folid Figures , are thofe that 162 EUCLID'S Elements :
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.