## 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 22

Side 36

... and because the straight line HG meets the parallels KM , FG ; the alternate

angles MHG , HGF are equal : ( 29. 1. ) add to each of these the angle HGL ;

therefore KHG , See

BOOK 1 .

... and because the straight line HG meets the parallels KM , FG ; the alternate

angles MHG , HGF are equal : ( 29. 1. ) add to each of these the angle HGL ;

therefore KHG , See

**Note**. the angles MHG , HGL are equal to the angles 36BOOK 1 .

Side 154

... See

ouvrages . THE ELEMENTS OF EUCLID . BOOK XI . DEFINITIONS . 154 BOOK

VI . THE ELEMENTS OF EUCLID .

... See

**Note**. + This is a Lemma of Cl . Ptolomæus , in page 9 of his pegaanouvrages . THE ELEMENTS OF EUCLID . BOOK XI . DEFINITIONS . 154 BOOK

VI . THE ELEMENTS OF EUCLID .

Side 177

... and are not in the same plane with the other two : wherefore they contain equal

angles ( 10. 11. ) ; the angle D * See

DCF ; and 23 BOOK XI . 177 THE ELEMENTS OF EUCLID being applied to the H

...

... and are not in the same plane with the other two : wherefore they contain equal

angles ( 10. 11. ) ; the angle D * See

**Note**. ABH is therefore equal to the angleDCF ; and 23 BOOK XI . 177 THE ELEMENTS OF EUCLID being applied to the H

...

Side 181

Therefore the solid AB is cut into two equal parts by the plane CDEF . Q. E. D. • N

. B. The insisting straight lines of a parallelopiped , mentioned * See

next and some following propositions , are the BOOK XI . 181 THE ELEMENTS ...

Therefore the solid AB is cut into two equal parts by the plane CDEF . Q. E. D. • N

. B. The insisting straight lines of a parallelopiped , mentioned * See

**Note**. in thenext and some following propositions , are the BOOK XI . 181 THE ELEMENTS ...

Side 184

the base CD to the same LQ : and because the solid parallelopiped AR is cut by

the plane LMEB , which * See

184 BOOK XI . THE ELEMENTS OF EUCLID .

the base CD to the same LQ : and because the solid parallelopiped AR is cut by

the plane LMEB , which * See

**Note**. is parallel to the opposite planes AK , DR ;184 BOOK XI . THE ELEMENTS OF EUCLID .

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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.