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

### Inni boken

Side 359

Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid Robert

Simson ... If a magnitude , together with a

ratio to another magnitude ; the excess of this other magnitude above a given ...

Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid Robert

Simson ... If a magnitude , together with a

**given magnitude**, See N. has a givenratio to another magnitude ; the excess of this other magnitude above a given ...

Side 361

Let the excess of the magnitude AB above a

to the magnitude BC ; the excess of AC , both of them together , above the

...

Let the excess of the magnitude AB above a

**given magnitude**have a given ratioto the magnitude BC ; the excess of AC , both of them together , above the

**given****magnitude**, has a given ratio to BC . Let AD be the**given magnitude**, the excess...

Side 365

therefore GB the excess of the sum EB above the

given ratio to the remainder FD . PROP . XXI . C. If two magnitudes have a given

ratio to one an- See N. other , if a

...

therefore GB the excess of the sum EB above the

**given magnitude**EG , has agiven ratio to the remainder FD . PROP . XXI . C. If two magnitudes have a given

ratio to one an- See N. other , if a

**given magnitude**be added to one of them , and...

Side 369

Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid Robert

Simson. Let AB , CD , EF be three magnitudes , and let GD the excess of one of

them CD above the

KD ...

Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid Robert

Simson. Let AB , CD , EF be three magnitudes , and let GD the excess of one of

them CD above the

**given magnitude**CG have a given ratio to AB ; and also letKD ...

Side 370

Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid Robert

Simson. 19 . PROP . XXVII . If there be three magnitudes , the excess of the first of

which above a

of ...

Viz. the First Six Books, Together with the Eleventh and Twelfth Euclid Robert

Simson. 19 . PROP . XXVII . If there be three magnitudes , the excess of the first of

which above a

**given magnitude**has a given ratio to the second ; and the excessof ...

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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...