Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund StoneD. Midwinter, 1728 |
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Página 10
... remaining will be equal . As if A + CBD , and AB ; then fhall C = D .. 4. If to unequal things you add equal things , the wholes will be unequal . As if AB and C = D ; then fhall A + CB + D . 5. If from unequal things you take away ...
... remaining will be equal . As if A + CBD , and AB ; then fhall C = D .. 4. If to unequal things you add equal things , the wholes will be unequal . As if AB and C = D ; then fhall A + CB + D . 5. If from unequal things you take away ...
Página 15
Euclid. qual to the Triangle ( bac ) ;, and the remaining An- gles ( B , C ) fhall be equal to the remaining Angles ( b , c ) each to each , under which the equal Sides are fubtended . If the Point a be applied to the Point A , and the ...
Euclid. qual to the Triangle ( bac ) ;, and the remaining An- gles ( B , C ) fhall be equal to the remaining Angles ( b , c ) each to each , under which the equal Sides are fubtended . If the Point a be applied to the Point A , and the ...
Página 27
... one Side of the other , either that Side AA which lies between the equal Angles , or that which is fubtended by one of the equal Angles : each remaining Side a 3. 1 . b fuppof . c hyp . Book I. 26 EUCLID'S Elements .
... one Side of the other , either that Side AA which lies between the equal Angles , or that which is fubtended by one of the equal Angles : each remaining Side a 3. 1 . b fuppof . c hyp . Book I. 26 EUCLID'S Elements .
Página 28
... remaining Side of the other ; and the remaining Angle of the one shall be equal to the remaining Angle of the other . Hyp . 1. Let BC = be ; I fay , BA = ba , and AC ac , and the Angle Abac . For if you fay that ba BA , make a bd BA ...
... remaining Side of the other ; and the remaining Angle of the one shall be equal to the remaining Angle of the other . Hyp . 1. Let BC = be ; I fay , BA = ba , and AC ac , and the Angle Abac . For if you fay that ba BA , make a bd BA ...
Página 31
... remaining Angle of the one , equal to the remaining Angle of the other . In like manner , if two Triangles have one Angle of the one , equal to one of the other ; then is the Sum of the remaining Angles of the one Triangle , equal to ...
... remaining Angle of the one , equal to the remaining Angle of the other . In like manner , if two Triangles have one Angle of the one , equal to one of the other ; then is the Sum of the remaining Angles of the one Triangle , equal to ...
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.