## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |

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Side iii

... c . and as

... c . and as

**these**may be acquired in a great measure from arithme , tic and geometry :**these**two sciences may truly be said to be the two great fountains from whence much of the wisdom and happiness of mankind flow : And therefore ... Side iv

As tyrants and arbitrary governours , immersed in pride , and stain'd with madness , are generally too stupid and brutal to be capable of understanding and esteeming

As tyrants and arbitrary governours , immersed in pride , and stain'd with madness , are generally too stupid and brutal to be capable of understanding and esteeming

**these**sciences , and their excellencies , and the major part of crafty ... Side v

... geometry , mechanics , and natural philosophy ; as also rational systems of morality , politics , and good government : certainly some or all of

... geometry , mechanics , and natural philosophy ; as also rational systems of morality , politics , and good government : certainly some or all of

**these**should be known , in a competent degree , more especially by all statesmen ... Side viii

The seventh , eighth , and ninth books are pretty short elements of arithmetic , and not of geometry ; altho '

The seventh , eighth , and ninth books are pretty short elements of arithmetic , and not of geometry ; altho '

**these**, with the rest , are altogether usually called Euclid's Elements of Geometry . The tenth book , being the Elements of ... Side ix

Accordingly

Accordingly

**these**eight books alone by most of the moderns have been looked upon as sufficient Elements of that plane and solid geometry , in use and fashion amongst us . If it should be asked , what occafion there was for publishing ...### Hva folk mener - Skriv en omtale

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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

### Populære avsnitt

Side 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.

Side 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...

Side 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.

Side 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.

Side 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.

Side 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.

Side 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...

Side 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Side 128 - When you have proved that the three angles of every triangle are equal to two right angles...

Side 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...