Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page xii
... Solid , & c . have no Ratio at all to one another , being quite incomparable according to Quantity . - Moreover , I do not know how juftly the Author of the Fifth Book can apply his Propofitions of it to fhew the Proportionality of ...
... Solid , & c . have no Ratio at all to one another , being quite incomparable according to Quantity . - Moreover , I do not know how juftly the Author of the Fifth Book can apply his Propofitions of it to fhew the Proportionality of ...
Page xiii
... Solids in the Eleventh and Twelfth Books , being Mag- nitudes of different Kinds . Because I must think all his Magnitudes in the Propofitions of the Fifth Book are agreeable to the Fourth Definition of it , and therefore they are all ...
... Solids in the Eleventh and Twelfth Books , being Mag- nitudes of different Kinds . Because I must think all his Magnitudes in the Propofitions of the Fifth Book are agreeable to the Fourth Definition of it , and therefore they are all ...
Page 312
... Solid is that which has length , breadth , and thick- nefs . 2. The bound of a folid is a fuperficies a . 3. A right line is perpendicular to a plane , when it makes right angles with all the right lines that touch it , and are drawn in ...
... Solid is that which has length , breadth , and thick- nefs . 2. The bound of a folid is a fuperficies a . 3. A right line is perpendicular to a plane , when it makes right angles with all the right lines that touch it , and are drawn in ...
Page 346
... Solid parallelepipedons , ftanding upon the fame base , and having the fame altitude , and whofe fides Standing upon the common bafe , terminate in the fame right lines , are equal to one another . For let the folid parallelepipedons CM ...
... Solid parallelepipedons , ftanding upon the fame base , and having the fame altitude , and whofe fides Standing upon the common bafe , terminate in the fame right lines , are equal to one another . For let the folid parallelepipedons CM ...
Page 347
... Solid parallelepipedons , having the fame base and al titude , and whofe fides ftanding upon the common bafe , do not terminate in the fame right lines , are equal to one another . For let the folid parallelepipedons CM . CN be upon the ...
... Solid parallelepipedons , having the fame base and al titude , and whofe fides ftanding upon the common bafe , do not terminate in the fame right lines , are equal to one another . For let the folid parallelepipedons CM . CN be upon the ...
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
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe 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...