## 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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Resultat 1-5 av 5

Side 124

Produce BD both ways to the points H , L , and take any number of straight lines

BG , GH , each equal to the

equal to the

are ...

Produce BD both ways to the points H , L , and take any number of straight lines

BG , GH , each equal to the

**base**BC ; and DK , KL , any number of them , eachequal to the

**base**CD , and join AG , AH , AK , AL : then , because CB , BG , GHare ...

Side 190

Ň Next , let the

then the solid AB is equal to the solid CD ... Make F then CT equal to AG , and

G T complete the solid parallelopiped CV of which the

Ň Next , let the

**bases**EH , NP not be equal ; but EH greater than the other : sincethen the solid AB is equal to the solid CD ... Make F then CT equal to AG , and

G T complete the solid parallelopiped CV of which the

**base**L P is NP , and the ... Side 191

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

( 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 209

Therefore the

solid which is less than the pyramid DEFH . In the same manner it may be

demonstrated , that the

to any ...

Therefore the

**base**ABC is not to the**base**DEF , as the pyramid ABCG to anysolid which is less than the pyramid DEFH . In the same manner it may be

demonstrated , that the

**base**DEF is not to the**base**ABC , as the pyramid DEFHto any ...

Side 210

are all the other antecedents to their common consequent : that is as the

ABCDE to the

, for the same reason , as the

are all the other antecedents to their common consequent : that is as the

**base**ABCDE to the

**base**FGH , so is the pyramid ABCDEM to the pyramid FGHN : and, for the same reason , as the

**base**FGHKL to the**base**FGH , so is the pyramid ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### 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.