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 19
these add the angle ACB , therefore the angles ACD , ACB are Book I. greater
than the angles ABC , ACB . but ACD , ACB are together equal o to two right
angles ; therefore the angles ABC , BCA are b . 13. I. less than two right angles .
in like ...
these add the angle ACB , therefore the angles ACD , ACB are Book I. greater
than the angles ABC , ACB . but ACD , ACB are together equal o to two right
angles ; therefore the angles ABC , BCA are b . 13. I. less than two right angles .
in like ...
Side 96
1 Book Iv . Let ABC be the given circle , and DEF the given triangle ; it is required
to inscribe in the circle ABC a ... HAC is equal < to the angle ABC in the alternate
segment of the circle . but HAC is equal to the angle DEF , therefore also the ...
1 Book Iv . Let ABC be the given circle , and DEF the given triangle ; it is required
to inscribe in the circle ABC a ... HAC is equal < to the angle ABC in the alternate
segment of the circle . but HAC is equal to the angle DEF , therefore also the ...
Side 418
IF : a triangle has a given obtuse angle ; the excess of the square of the side
which fubtends the obtufe angle above the squares of the sides which contain it ,
thall have a given ratio to the triangle . Let the triangle ABC have a given obtuse ...
IF : a triangle has a given obtuse angle ; the excess of the square of the side
which fubtends the obtufe angle above the squares of the sides which contain it ,
thall have a given ratio to the triangle . Let the triangle ABC have a given obtuse ...
Side 1
ET ABC be a rectilineal angle , if about the point B as a center , and with any
distance BA , a circle be described , meeting BA , BC , the straight lines including
the angle ABC in A , C ; the angle ABC will be to four right angles , as the arch AC
to ...
ET ABC be a rectilineal angle , if about the point B as a center , and with any
distance BA , a circle be described , meeting BA , BC , the straight lines including
the angle ABC in A , C ; the angle ABC will be to four right angles , as the arch AC
to ...
Side 24
of the angle ECF opposite to it , that is , in the triangle ABC , the co - fine of the
hypothenuse BC is to the radius , as the co - tangent ... Of these three , viz . the
hypothenuse and the two angles , any two being given , the third will also be
given .
of the angle ECF opposite to it , that is , in the triangle ABC , the co - fine of the
hypothenuse BC is to the radius , as the co - tangent ... Of these three , viz . the
hypothenuse and the two angles , any two being given , the third will also be
given .
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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 |