The Elements of Euclid |
Inni boken
Resultat 1-5 av 6
Side 101
Euclid Robert Simson. First, let GB be equal to E, HD is equal A to F : make CK
equal to F; and because AG is the same multiple of E, that CH is of F, and that GB
is equal to E, and CK to F; therefore AB is the same multiple of E, that KH is of F.
Euclid Robert Simson. First, let GB be equal to E, HD is equal A to F : make CK
equal to F; and because AG is the same multiple of E, that CH is of F, and that GB
is equal to E, and CK to F; therefore AB is the same multiple of E, that KH is of F.
Side 106
Euclid Robert Simson. proposition, there are some equimultiples of A and B, and
some multiple of C such, that the multiple of A is greater than the multiple of C,
but the multiple of B is not greater than that of C. Let such multiples be taken, and
...
Euclid Robert Simson. proposition, there are some equimultiples of A and B, and
some multiple of C such, that the multiple of A is greater than the multiple of C,
but the multiple of B is not greater than that of C. Let such multiples be taken, and
...
Side 255
... any multiple whatever of C; if the multiple of A be greater than the multiple of C,
then, by the 5th def. of book 5, the multiple of B is also greater than that of C ; but,
from the hypothesis that A has a greater ratio to C, than B has to C, there must, ...
... any multiple whatever of C; if the multiple of A be greater than the multiple of C,
then, by the 5th def. of book 5, the multiple of B is also greater than that of C ; but,
from the hypothesis that A has a greater ratio to C, than B has to C, there must, ...
Side 256
The above mentioned proposition, viz. If A have to C a greater ratio than B to C :
and if of A and B there be taken certain equimultiples, and some multiple | of C;
then if the multiple of B be greater than the multiple of C, the multiple of A is also ...
The above mentioned proposition, viz. If A have to C a greater ratio than B to C :
and if of A and B there be taken certain equimultiples, and some multiple | of C;
then if the multiple of B be greater than the multiple of C, the multiple of A is also ...
Side 257
... possible equimultiples of the second B, and of the fourth D, there can be found
some One multiple EF of the first A, and one IK of the second B, that are equal to
one another; and also, in the same case, 33 BOOK W. NOTEs. 257 PROP. XVIII.
... possible equimultiples of the second B, and of the fourth D, there can be found
some One multiple EF of the first A, and one IK of the second B, that are equal to
one another; and also, in the same case, 33 BOOK W. NOTEs. 257 PROP. XVIII.
Hva folk mener - Skriv en omtale
Vi har ikke funnet noen omtaler på noen av de vanlige stedene.
Andre utgaver - Vis alle
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 20 - ANY two angles of a triangle are together less than two right angles.
Bibliografisk informasjon
| Tittel | The Elements of Euclid |
| Forfatter | Euclid |
| Redaktør | Robert Simson |
| Utgiver | Desilver, Thomas & Company, 1838 |
| Original fra | University of Michigan |
| Digitalisert | 20. sep 2007 |
| Lengde | 416 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |