## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

### Inni boken

Side 308

B. V. The

depends upon this hypothesis , that to any three ... be

propositions preceding this : so far is it from deserving to be reckoned an axiom ,

as Clavius ...

B. V. The

**demonstration**of this is none of Euclid's , nor is it legitimate ; for itdepends upon this hypothesis , that to any three ... be

**demonstrated**by thepropositions preceding this : so far is it from deserving to be reckoned an axiom ,

as Clavius ...

Side 313

Book It seems plain , that some editor has changed the

gave of this proposition ; for , after he bas

equiangular to one another , he particularly shows that their sides about the

equal ...

Book It seems plain , that some editor has changed the

**demonstration**that Euclidgave of this proposition ; for , after he bas

**demonstrated**that the triangles areequiangular to one another , he particularly shows that their sides about the

equal ...

Side 316

5 , Book 8 , it is

, has to the plane number of which the sides are E , Z ( see Hervagius's or

Gregory's edition , ) the ratio which is compounded of the ratios of their sides ;

that is ...

5 , Book 8 , it is

**demonstrated**, that the plane number of which the sides are C , D, has to the plane number of which the sides are E , Z ( see Hervagius's or

Gregory's edition , ) the ratio which is compounded of the ratios of their sides ;

that is ...

Side 340

The angles ABH , DEM are

in the Greek : And in the same way ACH , DFM may be

angles : Also the repetition of the same

The angles ABH , DEM are

**demonstrated**to be right angles in a shorter way thanin the Greek : And in the same way ACH , DFM may be

**demonstrated**to be rightangles : Also the repetition of the same

**demonstration**, which begins with “ in ... Side 346

The

things are very explicitly

sufficiently explained ; for example , when it is affirmed , that the square of KB is

greater ...

The

**demonstration**of the proposition is spoiled and mutilated : For some easythings are very explicitly

**demonstrated**, while others not so obvious are notsufficiently explained ; for example , when it is affirmed , that the square of KB is

greater ...

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The Elements of Euclid: viz. the first six books, together with the eleventh ... Robert Simson Uten tilgangsbegrensning - 1835 |

The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Ingen forhåndsvisning tilgjengelig - 2019 |

The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Ingen forhåndsvisning tilgjengelig - 2019 |

### Vanlige uttrykk og setninger

ABCD added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter difference divided double draw drawn equal equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.

Side 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Side 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Side 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.

Side 153 - 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 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...

Side 28 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.

Side 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...