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 |
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Página 8
2. 1 . ! PRO P. IV . THEOREM . IF F two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another : they shall likewise have their ...
2. 1 . ! PRO P. IV . THEOREM . IF F two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another : they shall likewise have their ...
Página 9
A ' D Book I. gle BAC equal to the angle EDF . the base BC shall be eequal to the base EF ; and the triangle ABC to the ... Therefore if two triangles have two sides of the one equal to two sides of the other , each to each , and have ...
A ' D Book I. gle BAC equal to the angle EDF . the base BC shall be eequal to the base EF ; and the triangle ABC to the ... Therefore if two triangles have two sides of the one equal to two sides of the other , each to each , and have ...
Página 10
Because AF is equal to AG , and AB to AC ; the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triА. angles AFC , AGB ; therefore the base b . 4. 1 . FC is equal o to the ...
Because AF is equal to AG , and AB to AC ; the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triА. angles AFC , AGB ; therefore the base b . 4. 1 . FC is equal o to the ...
Página 11
Q. Let ABC be a triangle having the angle ABC equal to the Book 1 . angle ACB ; the fide AB is also equal to the side AC . ... one of them is greater than the other . let AB be the greater , and from it cut'off DB equal to AC , 2. 3.
Q. Let ABC be a triangle having the angle ABC equal to the Book 1 . angle ACB ; the fide AB is also equal to the side AC . ... one of them is greater than the other . let AB be the greater , and from it cut'off DB equal to AC , 2. 3.
Página 12
2. 5. I. Book 1 . But if one of the Vertices , as D , be within the other triangle MACB ; produce AC , AD to E , F. therefore B E because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD ...
2. 5. I. Book 1 . But if one of the Vertices , as D , be within the other triangle MACB ; produce AC , AD to E , F. therefore B E because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD ...
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Términos y frases comunes
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 fore four fourth given angle given in poſition given in ſpecies 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 reaſon rectangle rectangle contained rectilineal 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
Pasajes populares
Página 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.
Página 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.
Página 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Información bibliográfica
| Título | 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 |
| Autor | Robert Simson |
| Editor | A. Foulis, 1781 |
| Procedencia del original | Universidad de Michigan |
| Digitalizado | 11 Jun. 2007 |
| Largo | 466 páginas |
| Exportar cita | BiBTeX EndNote RefMan |