## 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 63

Let ABCD be a circle , of which the diaА в meter is AD , and the centre E ; and let

BC be nearer to the centre than FG ; AD is greater F than any straight line BC

which is not a

EK ...

Let ABCD be a circle , of which the diaА в meter is AD , and the centre E ; and let

BC be nearer to the centre than FG ; AD is greater F than any straight line BC

which is not a

**diameter**, and BC greater than FG . H From the centre draw EH ,EK ...

Side 145

If two similar parallelograms have a common angle , and be similarly situated ,

they are about the same

similar and similarly situated , and have the angle DAB common : ABCD and

AEFG are ...

If two similar parallelograms have a common angle , and be similarly situated ,

they are about the same

**diameter**. Let the parallelograms ABCD , AEFG besimilar and similarly situated , and have the angle DAB common : ABCD and

AEFG are ...

Side 232

sphere BCDE has to the

divided into the same number of pyramids , and in the same order , the pyramids

shall be similar to one another each to each ; because they have the solid angles

...

sphere BCDE has to the

**diameter**of the other sphere ; for if these two solids bedivided into the same number of pyramids , and in the same order , the pyramids

shall be similar to one another each to each ; because they have the solid angles

...

Side 354

ع milarly placed ; therefore EF is given in speG H F cies , and is about the same

therefore , because the L figure EF given in species is described upon the given ...

ع milarly placed ; therefore EF is given in speG H F cies , and is about the same

**diameter**( 26. 6. ) with DL ; let BCG be the**diameter**, and K construct the figure ;therefore , because the L figure EF given in species is described upon the given ...

Side 368

If from a given point in the

and from that point a straight line be drawn at right angles to the first , and from

the point in ...

If from a given point in the

**diameter**of a circle given in position , or in the**diameter**produced , a straight line be drawn to any point in the circumference ,and from that point a straight line be drawn at right angles to the first , and from

the point in ...

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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.