The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |
Inni boken
Resultat 1-5 av 8
Side 66
I. fore the base FG is equal d to the base FH . but besides FH no other straight
line can be drawn from F to D the circumference equal to FG . for H if there can ,
let it be FK , and because FK is equal to FG , and FG to FH , FK is equal to FH ,
that ...
I. fore the base FG is equal d to the base FH . but besides FH no other straight
line can be drawn from F to D the circumference equal to FG . for H if there can ,
let it be FK , and because FK is equal to FG , and FG to FH , FK is equal to FH ,
that ...
Side 67
Also there can be drawn only two equal straight lines from the point D to the
circumference , one upon each side of the least . at the point M in the straight line
MD , make the angle DMB equal to the angle DMK , and join DB . and because
MK ...
Also there can be drawn only two equal straight lines from the point D to the
circumference , one upon each side of the least . at the point M in the straight line
MD , make the angle DMB equal to the angle DMK , and join DB . and because
MK ...
Side 68
IT : F a point be taken within a circle , from which there fall more than two equal
straight lines to the circumference , that point is the center of the circle . Let the
point D be taken within the circle ABC , from which to the circumference there fall
...
IT : F a point be taken within a circle , from which there fall more than two equal
straight lines to the circumference , that point is the center of the circle . Let the
point D be taken within the circle ABC , from which to the circumference there fall
...
Side 183
Let ABC , DEF be equal circles ; and at their centers the angles BGC , EHF , and
the angles BAC , EDF at their circumferences . as the circumference BC to the
circumference EF , fo is the angle BGC to the angle EHF , and the angle BAC to
the ...
Let ABC , DEF be equal circles ; and at their centers the angles BGC , EHF , and
the angles BAC , EDF at their circumferences . as the circumference BC to the
circumference EF , fo is the angle BGC to the angle EHF , and the angle BAC to
the ...
Side 184
3 Book VI . the circumference EF , the same multiple is the angle EHN of the
nangle EHF . and if the circumference BL be equal to the circumfe . rence EN ,
the angle BGL is also equal to the angle EHN ; and if the circumference BL be
greater ...
3 Book VI . the circumference EF , the same multiple is the angle EHN of the
nangle EHF . and if the circumference BL be equal to the circumfe . rence EN ,
the angle BGL is also equal to the angle EHN ; and if the circumference BL be
greater ...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
Vanlige uttrykk og setninger
added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid angle fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
Populære avsnitt
Side 156 - 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 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
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 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
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.
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Side 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Bibliografisk informasjon
| Tittel | The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |
| Forfatter | Robert Simson |
| Utgiver | A. Foulis, 1781 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 466 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |