## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

### Inni boken

Side 190

... CV , so ( 32. 11. ) is the base EH to the base NP ; for the solids AB , CV are of

the same

parallelopipeds AB , CD are reciprocally proportional to their

the bases of the ...

... CV , so ( 32. 11. ) is the base EH to the base NP ; for the solids AB , CV are of

the same

**altitude**; and as the ... Wherefore , the bases of the solidparallelopipeds AB , CD are reciprocally proportional to their

**altitudes**. Let nowthe bases of the ...

Side 191

is the solid AB to the solid CV ; for the solids AB , CV are of the same

and as MC to CT , so is the base MP to the base PT , and the solid GD to the solid

( 25. 11. ) CV : and therefore as the solid AB to the solid CV , so is the solid CD to

...

is the solid AB to the solid CV ; for the solids AB , CV are of the same

**altitude**;and as MC to CT , so is the base MP to the base PT , and the solid GD to the solid

( 25. 11. ) CV : and therefore as the solid AB to the solid CV , so is the solid CD to

...

Side 213

to the solid EHPO : but the bases and

reciprocally proportional ( 34. ... the triangle ABC to the triangle DEF ; therefore

as the triangle ABC to the triangle DEF , so is the

...

to the solid EHPO : but the bases and

**altitudes**of equal solid parallelopipeds arereciprocally proportional ( 34. ... the triangle ABC to the triangle DEF ; therefore

as the triangle ABC to the triangle DEF , so is the

**altitude**of the solid EHPO to the...

Side 224

Either the

First , let them be equal : and the cylinders AX , EO , being also equal , and cones

and cylinders of the same

Either the

**altitude**MN is equal to the**altitude**KL , or these**altitudes**are not equal .First , let them be equal : and the cylinders AX , EO , being also equal , and cones

and cylinders of the same

**altitude**being to one another as their bases , ( 11. Side 225

consequently ES is a cylinder , the base of which is the circle EFHG , and

MP : and because the cylinder AX is equal to the cylinder EO , as AX is to the

cylinder ES , so ( 7. 5. ) is the cylinder EO to the same ES . But as the cylinder AX

to ...

consequently ES is a cylinder , the base of which is the circle EFHG , and

**altitude**MP : and because the cylinder AX is equal to the cylinder EO , as AX is to the

cylinder ES , so ( 7. 5. ) is the cylinder EO to the same ES . But as the cylinder AX

to ...

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure 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 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - 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 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.