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 6 - 10 από τα 51.
Σελίδα 47
... square of CD , is equal to the square of CB . pa- Book II . • Upon CB ... AC is equal to CB ; therefore alfo AL is e- qual to DF . to each of these ... square of CD . but the gnomon CMG and LG make up the whole figure CEFB , which is the ...
... square of CD , is equal to the square of CB . pa- Book II . • Upon CB ... AC is equal to CB ; therefore alfo AL is e- qual to DF . to each of these ... square of CD . but the gnomon CMG and LG make up the whole figure CEFB , which is the ...
Σελίδα 48
... square CEFD , join DE , and thro ' B b . 31. 1. drawb BHG parallel to CE or DF , and thro ' H draw KLM paral- lel to AD or EF , and also thro ' A draw AK parallel to CL or DM . and because AC is equal to CB , the rectangle AL is equal ...
... square CEFD , join DE , and thro ' B b . 31. 1. drawb BHG parallel to CE or DF , and thro ' H draw KLM paral- lel to AD or EF , and also thro ' A draw AK parallel to CL or DM . and because AC is equal to CB , the rectangle AL is equal ...
Σελίδα 49
... C ; the fquares of AB , BC are equal to twice the rectangle AB , BC together with the square of AC . b 1 Book II . Upon AB describe a the square ADEB , and construct the figure a . 46. I. as in the preceding Propofitions . and because ...
... C ; the fquares of AB , BC are equal to twice the rectangle AB , BC together with the square of AC . b 1 Book II . Upon AB describe a the square ADEB , and construct the figure a . 46. I. as in the preceding Propofitions . and because ...
Σελίδα 51
... C into two equal , and at D into two unequal parts . the fquares of AD , DB are together double of the squares of AC , CD . c ს From the point C draw a CE at right angles to AB , and make it a . 11. 1 . equal to AC or CB , and join EA ...
... C into two equal , and at D into two unequal parts . the fquares of AD , DB are together double of the squares of AC , CD . c ს From the point C draw a CE at right angles to AB , and make it a . 11. 1 . equal to AC or CB , and join EA ...
Σελίδα 52
... AC ; therefore the fquares of AE , EF are double of the squares of AC , CD . and the square of AF is equal to the fquares of AE , EF because AEF is a right angle ; therefore the fquare of AF is double of the fquares of AC , CD . but the ...
... AC ; therefore the fquares of AE , EF are double of the squares of AC , CD . and the square of AF is equal to the fquares of AE , EF because AEF is a right angle ; therefore the fquare of AF is double of the fquares of AC , CD . but the ...
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.