Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 204
For drawing the several semidiameters A L , BL , CL , & c these will divide the polygon into as many equal isosceles triangles as the figure has fides whose common perpendicular altitude will be the right line L K. Wherefore [ by 1. 2. ) ...
For drawing the several semidiameters A L , BL , CL , & c these will divide the polygon into as many equal isosceles triangles as the figure has fides whose common perpendicular altitude will be the right line L K. Wherefore [ by 1. 2. ) ...
Seite 240
The altitude of any figure is the perpendicular drawn from the vertex ( or top ] to the base b . s . A ratio is said to be compounded of ratios when the quantities of the fatios multiplied between themselves produce that ratioc .
The altitude of any figure is the perpendicular drawn from the vertex ( or top ] to the base b . s . A ratio is said to be compounded of ratios when the quantities of the fatios multiplied between themselves produce that ratioc .
Seite 242
Triangles and parallelograms which bave tbe fame altitude , have the same ratio to one another , as their bases d . : Let the triangles ABC , ACD , and the parallelograms EC , ce have the fame altitude , viz . the perpendicular drawn ...
Triangles and parallelograms which bave tbe fame altitude , have the same ratio to one another , as their bases d . : Let the triangles ABC , ACD , and the parallelograms EC , ce have the fame altitude , viz . the perpendicular drawn ...
Seite 243
Therefore triangles and parallelograms , which have the fame altitude , will have the same ratio to one another as their bafes . Whi Which was to be demonstrated . The demonstration of this propofition is one very natural and easy ...
Therefore triangles and parallelograms , which have the fame altitude , will have the same ratio to one another as their bafes . Whi Which was to be demonstrated . The demonstration of this propofition is one very natural and easy ...
Seite 244
But as the triangle BDE is to the triangle A DE , so is B D to DA : For since they have the fame altitude , viz . the perpendicular drawn from the point £ to A B , they are [ by 1. 6. ] to one another as their bases .
But as the triangle BDE is to the triangle A DE , so is B D to DA : For since they have the fame altitude , viz . the perpendicular drawn from the point £ to A B , they are [ by 1. 6. ] to one another as their bases .
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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
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Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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...