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 19
Side 12
1 , ther side of the base CD are equal ' to one another ; but the angle ECD is
greater than the angle BCD , wherefore the ... Therefore upon the fame base ,
and on the same side of it , there cannot be two triangles that have their sides
which are ...
1 , ther side of the base CD are equal ' to one another ; but the angle ECD is
greater than the angle BCD , wherefore the ... Therefore upon the fame base ,
and on the same side of it , there cannot be two triangles that have their sides
which are ...
Side 20
THE O R. Sec N. ANY two sides of a triangle are together greater a . 3. I. b . s.1 .
than the third side . Let ABC be a triangle ; any two sides of it together are greater
er than the third fi'e , viz . the files BA , AC greater than the side BC ; and AB , BC
...
THE O R. Sec N. ANY two sides of a triangle are together greater a . 3. I. b . s.1 .
than the third side . Let ABC be a triangle ; any two sides of it together are greater
er than the third fi'e , viz . the files BA , AC greater than the side BC ; and AB , BC
...
Side 23
Of the two sides DE , DF let DE be the side which is not greater than the other ,
and at the point D in the straight line DE make the angle EDG equal to the angle
BAC ; and make DG a . 23. 1 . equal b to AC or DF , and join EG , GF . b . 3 , .
Of the two sides DE , DF let DE be the side which is not greater than the other ,
and at the point D in the straight line DE make the angle EDG equal to the angle
BAC ; and make DG a . 23. 1 . equal b to AC or DF , and join EG , GF . b . 3 , .
Side 31
gles o , each to each , to which the equal sides are opposite . there- Book I. fore
the angle ACB is equal to the angle CBD . and because the n straight line BC
meets the two straight lines AC , BD and makes b . 4. I. the alternate angles ACB
...
gles o , each to each , to which the equal sides are opposite . there- Book I. fore
the angle ACB is equal to the angle CBD . and because the n straight line BC
meets the two straight lines AC , BD and makes b . 4. I. the alternate angles ACB
...
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 ... and because MK is equal to MB ,
and MD common to the triangles KMD , BMD , the two sides KM , MD are equal to
the ...
Also there can be drawn only two equal straight lines from the point D to the
circumference , one upon each side of the ... and because MK is equal to MB ,
and MD common to the triangles KMD , BMD , the two sides KM , MD are equal to
the ...
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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 |