Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 10
... because A B is equal to DE : But fince F the right line A B agrees with D E , the right line A c fhall also agree with DF , because the angle BAC is equal to the angle EDF . Wherefore the point c will agree with the point F , because ...
... because A B is equal to DE : But fince F the right line A B agrees with D E , the right line A c fhall also agree with DF , because the angle BAC is equal to the angle EDF . Wherefore the point c will agree with the point F , because ...
Page 12
... Because the latter part was the less important and useful part of the propofition , and there- fore the former part deferved the first place . And if a propo- fition be not all Euclid's , because it is not useful in all its parts ...
... Because the latter part was the less important and useful part of the propofition , and there- fore the former part deferved the first place . And if a propo- fition be not all Euclid's , because it is not useful in all its parts ...
Page 13
... because AC is equal to AD , the angle A CD is equal to the angle ADC [ by prop . 5. ] wherefore the angle ADC is greater than the angle DC B , and the angle CDB is much greater than the angle DC B. Again , because the right line CB is ...
... because AC is equal to AD , the angle A CD is equal to the angle ADC [ by prop . 5. ] wherefore the angle ADC is greater than the angle DC B , and the angle CDB is much greater than the angle DC B. Again , because the right line CB is ...
Page 17
... because the fide A C is equal to the fide C B , and the fide CD is com- mon ; the two fides A C , C D are equal A to the two fides B C , C D , each to each ; and the angle A C D is equal to the angle B CD : therefore the bafe AD [ by ...
... because the fide A C is equal to the fide C B , and the fide CD is com- mon ; the two fides A C , C D are equal A to the two fides B C , C D , each to each ; and the angle A C D is equal to the angle B CD : therefore the bafe AD [ by ...
Page 23
... because the fide A c is A greater than the fide A B , put [ by prop . 3. ] the right line A D equal to the fide A B , and draw the right line BD : Then because ADB is an outward angle of the triangle BDC , itis greater [ by prop . 16 ...
... because the fide A c is A greater than the fide A B , put [ by prop . 3. ] the right line A D equal to the fide A B , and draw the right line BD : Then because ADB is an outward angle of the triangle BDC , itis greater [ by prop . 16 ...
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...