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
Now this Proposition is a Theorem , not a Definition ; because the equality of
figures of any kind muft be demonstrated , and not alsumed ; and therefore ,
though this were a true Proposition , it ought to have been demonstrated . But ,
indeed ...
Now this Proposition is a Theorem , not a Definition ; because the equality of
figures of any kind muft be demonstrated , and not alsumed ; and therefore ,
though this were a true Proposition , it ought to have been demonstrated . But ,
indeed ...
Side 307
Prop . but not from this that E , G , F , H are proportionals , for this last is the
conclusion of the Proposition . Wherefore these words « because it is
demonstrated , " & c . are wholly foreign to his design , and he should have
proved that if K be ...
Prop . but not from this that E , G , F , H are proportionals , for this last is the
conclusion of the Proposition . Wherefore these words « because it is
demonstrated , " & c . are wholly foreign to his design , and he should have
proved that if K be ...
Side 308
B. V. There are two cases of this Proposition , of which only the first and simplest
is demonstrated in the Greek . and it is probable Theon thought it was sufficient to
give this one , since he was to make use of neither of them in his mutilated ...
B. V. There are two cases of this Proposition , of which only the first and simplest
is demonstrated in the Greek . and it is probable Theon thought it was sufficient to
give this one , since he was to make use of neither of them in his mutilated ...
Side 314
Prop . and both cases of the 6. are neceffary , and these two Propositions are the
converses of the I. and 2. Now the 5. and 6. do not enter into the demonstration of
any Proposition in this Book as we now have it , nor can they be of use in any ...
Prop . and both cases of the 6. are neceffary , and these two Propositions are the
converses of the I. and 2. Now the 5. and 6. do not enter into the demonstration of
any Proposition in this Book as we now have it , nor can they be of use in any ...
Side 316
Therefore the Axiom , [ i . e . the Proposition before set down , ] « remains
demonstrated , " & c . Not in the leaft ; but it remains still undemonstrated : for
what he says may happen , may in innumerable cafes never happen , and
therefore his ...
Therefore the Axiom , [ i . e . the Proposition before set down , ] « remains
demonstrated , " & c . Not in the leaft ; but it remains still undemonstrated : for
what he says may happen , may in innumerable cafes never happen , and
therefore his ...
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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 |