Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite iii
Accordingly , since wisdom is so necessary to happiness , that learning , which is best adapted to promote and extend it , is undoubtedly the most valuable , and ought by all to be most encouraged , cultivated , and used .
Accordingly , since wisdom is so necessary to happiness , that learning , which is best adapted to promote and extend it , is undoubtedly the most valuable , and ought by all to be most encouraged , cultivated , and used .
Seite vi
Hence , since it is demonstrable that the happiness and preservation of a society is aug mented by the greater quantity of veracity dispersed throughout the individuals of that society , for lying and deceit tend to destroy it ...
Hence , since it is demonstrable that the happiness and preservation of a society is aug mented by the greater quantity of veracity dispersed throughout the individuals of that society , for lying and deceit tend to destroy it ...
Seite 6
Since two right lines A B , CD in the same plane , must necessarily meet or be parallel ; and if they ... If both the angles E , F on the right were less than both the angles A E F , CFE on the left ; and since two different right lines ...
Since two right lines A B , CD in the same plane , must necessarily meet or be parallel ; and if they ... If both the angles E , F on the right were less than both the angles A E F , CFE on the left ; and since two different right lines ...
Seite 10
... then shall the point B agree with the point E ; because A B is equal to de : But since B CE F the right line A B agrees with DE , the right line a c shall also agree with DF , because the angle Bac is equal to the angle EDF .
... then shall the point B agree with the point E ; because A B is equal to de : But since B CE F the right line A B agrees with DE , the right line a c shall also agree with DF , because the angle Bac is equal to the angle EDF .
Seite 11
But since the whole line AF is equal to the whole line A G , and A B is equal to AC ; therefore the remainder BF will be equal to the remainder cGx [ by ax . 3. ) But it has been proved , that the right line fc is equal to the right ...
But since the whole line AF is equal to the whole line A G , and A B is equal to AC ; therefore the remainder BF will be equal to the remainder cGx [ by ax . 3. ) But it has been proved , that the right line fc is equal to the right ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
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...