Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 39
... diameter bisects it " . Let there be a parallelogram ACDB , and its diameter BC : I say , the opposite sides and angles of the parallelo- gram ACDB are equal , and a diameter divides it into two equal parts . For because A B is parallel ...
... diameter bisects it " . Let there be a parallelogram ACDB , and its diameter BC : I say , the opposite sides and angles of the parallelo- gram ACDB are equal , and a diameter divides it into two equal parts . For because A B is parallel ...
Page 40
... diameter bisects it . For because A B is equal to c D , and в с is common ; the two fides AB , BC are each equal to the two fides DC , CB , and the angle ABC is equal to the angle BCD : Therefore the base A C [ by prop . 4. ] is equal ...
... diameter bisects it . For because A B is equal to c D , and в с is common ; the two fides AB , BC are each equal to the two fides DC , CB , and the angle ABC is equal to the angle BCD : Therefore the base A C [ by prop . 4. ] is equal ...
Page 43
... diameter A B cuts into halves , and the triangle DBC the one half of the parallelogram DBCF ; because [ by prop . 34. ] the diameter DC cuts it into halves . But the halves of equal things are themselves equal ; therefore the triangle ...
... diameter A B cuts into halves , and the triangle DBC the one half of the parallelogram DBCF ; because [ by prop . 34. ] the diameter DC cuts it into halves . But the halves of equal things are themselves equal ; therefore the triangle ...
Page 45
... diameter A C [ by prop . 34. ] cuts it into halves : wherefore the parallelogram ABCD will be double to the triangle E в с . ) BC E If therefore a parallelogram and a triangle have the fame base , and are between the fame parallels ...
... diameter A C [ by prop . 34. ] cuts it into halves : wherefore the parallelogram ABCD will be double to the triangle E в с . ) BC E If therefore a parallelogram and a triangle have the fame base , and are between the fame parallels ...
Page 46
... diameter , are equal to one another " . Let there be a parallelogram A B CD , whose diameter is Ac ; and let the parallelograms EH , FG be about the fame ; then BK , KD are called the complements of them : I fay , the complement BK is ...
... diameter , are equal to one another " . Let there be a parallelogram A B CD , whose diameter is Ac ; and let the parallelograms EH , FG be about the fame ; then BK , KD are called the complements of them : I fay , the complement BK is ...
Other editions - View all
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |
Common terms and phrases
alſo angle ABC becauſe the angle biſected centre circle ABCD circumference cone conſequent conſtruction cylinder demonftrated deſcribed diameter equal angles equal fides equiangular equimultiples Euclid fame altitude fame ratio fame reaſon fides A B fimilar fince firſt fixth fore four right given circle given right line given triangle greater inſcribed interfect join leſs oppoſite parallel parallelepipedon parallelogram perpendicular plane point F polygon priſms PROP proportional propoſition rectangle rectangle contained remaining angle right angles right line A B right lined figure right-lined ſame ſame multiple ſay SCHOLIUM ſecond ſector ſegment ſemidiameter ſhall ſide ſince ſolid ſome ſphere ſquares of A C ſtand ſuch ſum THEOR theſe thoſe thro trapezium triangle ABC twice the ſquare vertex the point Wherefore whoſe baſe
Popular passages
Page 247 - 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.
Page 30 - 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...
Page 248 - 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.
Page 18 - 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.
Page 32 - 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.
Page 56 - 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.
Page 391 - 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...
Page 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 183 - 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...