Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Página 74
... one of them is cut or divided into any parts whatsoever , the reEtangle contained under the two right lines is equal to all the rectangles contained under the undivided line , and the several segments or parts of the other line .
... one of them is cut or divided into any parts whatsoever , the reEtangle contained under the two right lines is equal to all the rectangles contained under the undivided line , and the several segments or parts of the other line .
Página 75
... if a right line be cut or divided into any parts soever , the rectangle contained under the two right lines is equal to all the rectangles contained under the undivided line , and the several segments or parts of the divided line .
... if a right line be cut or divided into any parts soever , the rectangle contained under the two right lines is equal to all the rectangles contained under the undivided line , and the several segments or parts of the divided line .
Página 82
... e B also will be equal to the right line A D , for E a is equal to DB and A B is common to both . Therefore [ by 5. 2 . . ] the rectangle under the unequal parts E B , BD , together with the square of the intermediate segment C B ...
... e B also will be equal to the right line A D , for E a is equal to DB and A B is common to both . Therefore [ by 5. 2 . . ] the rectangle under the unequal parts E B , BD , together with the square of the intermediate segment C B ...
Página 92
... together with twice the retangle under the base and that segment of it ( made by the falling of the perpendicular upon it ) which lies under the remaining Jade containin ; the obtufo angle , will be cqual to the Square of this ...
... together with twice the retangle under the base and that segment of it ( made by the falling of the perpendicular upon it ) which lies under the remaining Jade containin ; the obtufo angle , will be cqual to the Square of this ...
Página 94
If a perpendicular be drawn from the opposite angle of any triangle upon the base , making two segmests therezzpor , the square of one of the files , together with the square of thai segment next to the other side , will be equal to the ...
If a perpendicular be drawn from the opposite angle of any triangle upon the base , making two segmests therezzpor , the square of one of the files , together with the square of thai segment next to the other side , will be equal to the ...
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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...