## 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 11

Side 36

Ax . ) if produced far enough : therefore HB , FE shall meet ; if produced ; let them

meet in K , and through K , draw KL parallel to EA or FH , and produce HA , GB to

the points LM : then HLKF is a

Ax . ) if produced far enough : therefore HB , FE shall meet ; if produced ; let them

meet in K , and through K , draw KL parallel to EA or FH , and produce HA , GB to

the points LM : then HLKF is a

**parallelogram**, of which the diameter is HK , and ... Side 143

BCD equal to the angle ECG : the ratio of the

their sides . Let BG , CG , be placed in a straight line ; therefore DC and CE are

also in a ...

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 oftheir sides . Let BG , CG , be placed in a straight line ; therefore DC and CE are

also in a ...

Side 145

to the

equal to D ; and it is similar to ABC . Therefore ... If two similar

have a common angle , and be similarly situated , they are about the same

diameter .

to the

**parallelogram**EF : but EF is equal to the figure D ; wherefore also KGH isequal to D ; and it is similar to ABC . Therefore ... If two similar

**parallelograms**have a common angle , and be similarly situated , they are about the same

diameter .

Side 147

X To a given straight line to apply a

figure , and deficient by a

given rectilineal figure to which the

must ...

X To a given straight line to apply a

**parallelogram**equal to a given rectilinealfigure , and deficient by a

**parallelogram**similar to a given**parallelogram**: but thegiven rectilineal figure to which the

**parallelogram**to be applied is to be equal ,must ...

Side 177

If a solid be contained by six planes , two and two of which are parallel ; the

opposite planes are similar and equal

contained by the parallel planes AC , GF ; BG , CE ; FB , AE : its opposite planes

are ...

If a solid be contained by six planes , two and two of which are parallel ; the

opposite planes are similar and equal

**parallelograms**. * Let the solid CDGH becontained by the parallel planes AC , GF ; BG , CE ; FB , AE : its opposite planes

are ...

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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.