The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |
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Αποτελέσματα 1 - 5 από τα 68.
Σελίδα 60
... A fegment of a circle is the figure con- tained by a straight line and the cir- cumference it cuts off . VII . " The angle of a segment is that which is contained by the ftraight " line and the circumference . " VIII . An angle in a ...
... A fegment of a circle is the figure con- tained by a straight line and the cir- cumference it cuts off . VII . " The angle of a segment is that which is contained by the ftraight " line and the circumference . " VIII . An angle in a ...
Σελίδα 61
... circle ABC . Which was to be found . COR . From this it is manifeft , that if in a circle a straight line bisect another at right angles , the center of the circle is in the line which bifects the other . d.io.Def.1 . PROP . II . THEOR ...
... circle ABC . Which was to be found . COR . From this it is manifeft , that if in a circle a straight line bisect another at right angles , the center of the circle is in the line which bifects the other . d.io.Def.1 . PROP . II . THEOR ...
Σελίδα 63
... a ftraight line , & c . Q. E. D. PROP . IV . THEOR . F in a circle two straight lines cut one another which do not both pass thro ' the center , they do not bi- fect each the other . Let ABCD be a circle , and AC , BD two straight lines ...
... a ftraight line , & c . Q. E. D. PROP . IV . THEOR . F in a circle two straight lines cut one another which do not both pass thro ' the center , they do not bi- fect each the other . Let ABCD be a circle , and AC , BD two straight lines ...
Σελίδα 64
... circles ABC , CDE touch one another internally in the point C. they have not the fame center . For if they can , let it be F ; join FC , and draw any straight line FEB meeting them in E and B. and because F is the center of the circle ABC ...
... circles ABC , CDE touch one another internally in the point C. they have not the fame center . For if they can , let it be F ; join FC , and draw any straight line FEB meeting them in E and B. and because F is the center of the circle ABC ...
Σελίδα 65
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the center . let the center be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the center . let the center be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
Συχνά εμφανιζόμενοι όροι και φράσεις
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone conſtruction cylinder defcribed demonſtrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fhewn fides fides BA fimilar fince firft firſt folid angle fore fquare fquare of AC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular plane angles PROP Propofition pyramid rectangle contained rectilineal figure right angles ſame ſhall ſpace ſphere ſquare ſtraight line AB THEOR theſe thro tiple triangle ABC wherefore
Δημοφιλή αποσπάσματα
Σελίδα 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.
Σελίδα 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.
Σελίδα 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 163 - 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.
Σελίδα 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.