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 112
C than that of the second , the multiple of the third is also greater than that of the
fourth . VI . Magnitudes which have the same ratio are called proportionals . N. B.
“ When four magnitudes are proportionals , it is usually expressed by saying , the
...
C than that of the second , the multiple of the third is also greater than that of the
fourth . VI . Magnitudes which have the same ratio are called proportionals . N. B.
“ When four magnitudes are proportionals , it is usually expressed by saying , the
...
Side 114
Ex aequali , from equality ; this term is used simply by itself , when the first
magnitude is to the second of the first rank , as the first to the second of the other
rank ; and as the second is to the third of the first rank , fo is the second to the
third of ...
Ex aequali , from equality ; this term is used simply by itself , when the first
magnitude is to the second of the first rank , as the first to the second of the other
rank ; and as the second is to the third of the first rank , fo is the second to the
third of ...
Side 116
I F the first magnitude be the same . multiple of the second that the third is of the
fourth , and the fifth the fame multiple of the second that the sixth is of the fourth ;
then shall the first together with the fifth be the same multiple of the second , that ...
I F the first magnitude be the same . multiple of the second that the third is of the
fourth , and the fifth the fame multiple of the second that the sixth is of the fourth ;
then shall the first together with the fifth be the same multiple of the second , that ...
Side 121
A. THEOR . IN F the first of four magnitudes has to the second , the See N. same
ratio which the third has to the fourth ; then if the first be greater than the second ,
the third is also greater than the fourth ; and if equal , equal ; if less , less .
A. THEOR . IN F the first of four magnitudes has to the second , the See N. same
ratio which the third has to the fourth ; then if the first be greater than the second ,
the third is also greater than the fourth ; and if equal , equal ; if less , less .
Side 308
That if four magnitudes be “ proportionals , the third must necessarily be greater
than the “ fourth , when the first is greater than the second ; as Clavius
acknowledges in the 16. Prop . of the 5. Book of the Elements . " But tho ' Clavius
makes ...
That if four magnitudes be “ proportionals , the third must necessarily be greater
than the “ fourth , when the first is greater than the second ; as Clavius
acknowledges in the 16. Prop . of the 5. Book of the Elements . " But tho ' Clavius
makes ...
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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 |