Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página 5
That a circle may be described from any centre to any distance . COMMON NOTIONS or AXIOMS . 1. Things equal to the same thing , are equal to one another . 2. If equal things be added to equal things , the wholes are equal . 3.
That a circle may be described from any centre to any distance . COMMON NOTIONS or AXIOMS . 1. Things equal to the same thing , are equal to one another . 2. If equal things be added to equal things , the wholes are equal . 3.
Página 7
ET A B be a given finite right line : it is required to constitute an equilateral triangle upon the right line A B. From the centre A , with the distance A B , let the circle BC D be described [ by poftul . 3. ) ...
ET A B be a given finite right line : it is required to constitute an equilateral triangle upon the right line A B. From the centre A , with the distance A B , let the circle BC D be described [ by poftul . 3. ) ...
Página 8
at the point a a right line A D , equal to the right : line c ' ; " and from the centie A , with the distance a D , let a circle Det A be described [ by post . 3. ] . And because the point A is the centre of the circle D F E , the right ...
at the point a a right line A D , equal to the right : line c ' ; " and from the centie A , with the distance a D , let a circle Det A be described [ by post . 3. ] . And because the point A is the centre of the circle D F E , the right ...
Página 16
... if an isosceles triangle Def were described or constructed upon the right line DE , having one of its equal fides DF or E F equal to AD or A E. Hence it appears , how any given angle may be divided into 4 , 8 , 16 , 32 , & c . equal ...
... if an isosceles triangle Def were described or constructed upon the right line DE , having one of its equal fides DF or E F equal to AD or A E. Hence it appears , how any given angle may be divided into 4 , 8 , 16 , 32 , & c . equal ...
Página 18
Let any point o be taken on the other side of the line AB ; and about the centre c , F with the distance c D , let the circle E F G be described [ by poft . 3. ) ...
Let any point o be taken on the other side of the line AB ; and about the centre c , F with the distance c D , let the circle E F G be described [ by poft . 3. ) ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone continue cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore four fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe
Pasajes populares
Página 245 - 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 28 - If two triangles have two angles of the 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 equal...
Página 246 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.
Página 16 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Página 30 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.
Página 54 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 389 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...
Página 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Página 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 181 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...