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 285
... the triplicate ratio of that which the diameter EF has to the diameter BC . but as
the sphere LMN to ABC , so is the sphere DEF to some sphere , which must be
less than the sphere ABC , because the sphere LMN is greater than the sphere ...
... the triplicate ratio of that which the diameter EF has to the diameter BC . but as
the sphere LMN to ABC , so is the sphere DEF to some sphere , which must be
less than the sphere ABC , because the sphere LMN is greater than the sphere ...
Side 293
... yet it is science which must give the reason why two sides of a triangle are
greater than the third . but the right answer to ... is , that the number of Axioms
ought not to be encreased without necessity , as it must be if these Propositions
be not ...
... yet it is science which must give the reason why two sides of a triangle are
greater than the third . but the right answer to ... is , that the number of Axioms
ought not to be encreased without necessity , as it must be if these Propositions
be not ...
Side 294
Book I. that these circles must meet one another , because FD and GH are
together greater than FG ? and this determination is easier to be understood than
that which Mr. Thomas Simpson derives from it , and puts instead of Euclid's , in
the ...
Book I. that these circles must meet one another , because FD and GH are
together greater than FG ? and this determination is easier to be understood than
that which Mr. Thomas Simpson derives from it , and puts instead of Euclid's , in
the ...
Side 300
... it is neceffary that the point found by the construction of the Problem be proved
to be the center of the circle , by the help of this Definition , and some of the
preceding propositions , and because in the Demonstration , this Proposition
must be ...
... it is neceffary that the point found by the construction of the Problem be proved
to be the center of the circle , by the help of this Definition , and some of the
preceding propositions , and because in the Demonstration , this Proposition
must be ...
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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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 |