## 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 |

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Side 214

EVERY cone is a third part of a

equal altitude with it . Let a cone have the same base with a

circle ABCD , and the same altitude . The cone is the third part of the

that is ...

EVERY cone is a third part of a

**cylinder**which has the same base , and is of anequal altitude with it . Let a cone have the same base with a

**cylinder**, viz . thecircle ABCD , and the same altitude . The cone is the third part of the

**cylinder**;that is ...

Side 222

the

the same base , and of the same altitude : therefore also the

the

**cylinder**to the**cylinder**' ; for every cone is the third part of the**cylinder**uponthe same base , and of the same altitude : therefore also the

**cylinder**has to the**cylinder**the triplicate ratio of that which AC has to EG . Wherefore similar cones ... Side 223

02 z it is to be shown , that the

the axis KF . Produce the axis EF both ways ; and take any number of straight

lines EN , NL , each equal to EK ; and any number FX , XM each equal to FK ;

and ...

02 z it is to be shown , that the

**cylinder**AH is to the**cylinder**HC , as the axis EK tothe axis KF . Produce the axis EF both ways ; and take any number of straight

lines EN , NL , each equal to EK ; and any number FX , XM each equal to FK ;

and ...

Side 224

therefore also the

cut by the plane CD parallel to its opposite planes , as the -F K

therefore also the

**cylinders**EB , CM are equal . And because the**cylinder**FM iscut by the plane CD parallel to its opposite planes , as the -F K

**cylinder**CM to the**cylinder**FD , SO is ( 13. 12. ) the axis LN to the axis KL . But the**cylinder**CM is ... Side 225

consequently ES is a

MP : and because the

the

consequently ES is a

**cylinder**, the base of which is the circle EFHG , and altitudeMP : and because the

**cylinder**AX is ... is the base ABCD to the base EFGH ; forthe

**cylinders**AX , ES are of the same altitude ; and as the**cylinder**EO to the ...### Hva folk mener - Skriv en omtale

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

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### 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.