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 12
The case in which the Vertex of one triangle is upon a side of the other , needs no
demonstration . Therefore upon the fame base , and on the same side of it , there
cannot be two triangles that have their sides which are terminated in one ...
The case in which the Vertex of one triangle is upon a side of the other , needs no
demonstration . Therefore upon the fame base , and on the same side of it , there
cannot be two triangles that have their sides which are terminated in one ...
Side 20
6 than the angle ACB ; but it is not ; therefore the side AC is not less than AB . and
it has been shewn that it is not equal to b ... Let ABC be a triangle ; any two sides
of it together are greater than the third fide , viz . the sides BA , AC greater than ...
6 than the angle ACB ; but it is not ; therefore the side AC is not less than AB . and
it has been shewn that it is not equal to b ... Let ABC be a triangle ; any two sides
of it together are greater than the third fide , viz . the sides BA , AC greater than ...
Side 24
F two triangles have two angles of one equal to two angles of the other ; each to
each , and one side equal to one side , viz . either the sides adjacent to the equat
angles , or the sides opposite to equal angles in each ; then shall the other sides
...
F two triangles have two angles of one equal to two angles of the other ; each to
each , and one side equal to one side , viz . either the sides adjacent to the equat
angles , or the sides opposite to equal angles in each ; then shall the other sides
...
Side 31
T " THE opposite sides and angles of parallelograms are equal to one another ,
and the diameter bifects them , that is , divides them into two equal parts . N. B. A
Parallelogram is a four sided figure of which the opposite sides are parallel . and
...
T " THE opposite sides and angles of parallelograms are equal to one another ,
and the diameter bifects them , that is , divides them into two equal parts . N. B. A
Parallelogram is a four sided figure of which the opposite sides are parallel . and
...
Side 269
... and therefore , the sides about the right angles OKL , SMN being proportionals
, the triangle LKQ is similar to the triangle NMS . and because of the fimilarity of
the triangles AKL , EMN , as LA is to AK , so is NE to EM ; and by the similarity of ...
... and therefore , the sides about the right angles OKL , SMN being proportionals
, the triangle LKQ is similar to the triangle NMS . and because of the fimilarity of
the triangles AKL , EMN , as LA is to AK , so is NE to EM ; and by the similarity of ...
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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 |