The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |
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Side 381
IF F a straight line be drawn to a given point in a given straight line , and makes a
given angle with it . that straight line is given in position . Let AB be a straight line
given in position , and C a given point in it , the straight line drawn to C which ...
IF F a straight line be drawn to a given point in a given straight line , and makes a
given angle with it . that straight line is given in position . Let AB be a straight line
given in position , and C a given point in it , the straight line drawn to C which ...
Side 384
1 H and if G be equal to HK , EF also is equal to it ; wherefore EP is at right
angles to CD , for if it be not , EF would be greater than HK , which is absurd .
therefore the angle EFD is a right and consequently a given angle . But if the
straight lire ...
1 H and if G be equal to HK , EF also is equal to it ; wherefore EP is at right
angles to CD , for if it be not , EF would be greater than HK , which is absurd .
therefore the angle EFD is a right and consequently a given angle . But if the
straight lire ...
Side 392
See N. F a triangle has one of its angles which is not a right have a given ratio to
one another ; the triangle is given in species . a . 32 I. Let the triangle ABC have
one of its angles ABC a given , but not a right angle , and let the sides BA , AC ...
See N. F a triangle has one of its angles which is not a right have a given ratio to
one another ; the triangle is given in species . a . 32 I. Let the triangle ABC have
one of its angles ABC a given , but not a right angle , and let the sides BA , AC ...
Side 426
Describe the circle BAC about the triangle , and from its center E draw EA , EB ,
EC , ED . because the angle BAC is given , the b . 20. 3. angle BEC at the center ,
which is the double 6 of it , is given . and the ratio of BE to EC is given , because ...
Describe the circle BAC about the triangle , and from its center E draw EA , EB ,
EC , ED . because the angle BAC is given , the b . 20. 3. angle BEC at the center ,
which is the double 6 of it , is given . and the ratio of BE to EC is given , because ...
Side 445
E , and join EC . the angle , ACE being a right angle is given ; and the angle AEC
B is given ; therefore c the triangle ACE is E given in species , and the ratio of EA
to AC is therefore given . and EA is givendin magd . 5. Def . nitude , because ...
E , and join EC . the angle , ACE being a right angle is given ; and the angle AEC
B is given ; therefore c the triangle ACE is E given in species , and the ratio of EA
to AC is therefore given . and EA is givendin magd . 5. Def . nitude , because ...
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Vanlige uttrykk og setninger
added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 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.
Side 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.
Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 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.
Side 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.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth The Elements of Euclid: Also the Book of Euclid's Data ...cor. Viz. The First Six Books, Together with the Eleventh and Twelfth, Robert Simson |
| Forfatter | Robert Simson |
| Utgiver | F. Wingrave, 1804 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Eksporter sitat | BiBTeX EndNote RefMan |