## 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 9

Side 44

to HF ; therefore also AL is equal to HF : to each of these add CM ; therefore the

by AD , DB , for DM is equal ( Cor . 4. 2. ) to DB : therefore the gnomon CMG is ...

to HF ; therefore also AL is equal to HF : to each of these add CM ; therefore the

**whole**AM is equal to the E G F gnomon CMG : and DM is the rectangle containedby AD , DB , for DM is equal ( Cor . 4. 2. ) to DB : therefore the gnomon CMG is ...

Side 86

... one of which cuts , and the other meets the circle , and that the rectangle AB , A

BC contained by the

is equal to the square of BD which meets it ; the straight line BD touches С ( 34.

... one of which cuts , and the other meets the circle , and that the rectangle AB , A

BC contained by the

**whole**of the cutting line , and the part of it without the circleis equal to the square of BD which meets it ; the straight line BD touches С ( 34.

Side 114

from the first , is to a magnitude taken from the other ; the remainder shall be to

the remainder , as the

, as AE , a magnitude taken from AB , to CF , a magnitude taken from CD ; the ...

from the first , is to a magnitude taken from the other ; the remainder shall be to

the remainder , as the

**whole**to the**whole**. * Let the**whole**AB be to the**whole**CD, as AE , a magnitude taken from AB , to CF , a magnitude taken from CD ; the ...

Side 146

Let AB be a straight line divided into equal parts in C ; and let the parallelogram

AD be applied to the half AC , which is therefore defi . cient from the

parallelogram upon the

half CB : of all ...

Let AB be a straight line divided into equal parts in C ; and let the parallelogram

AD be applied to the half AC , which is therefore defi . cient from the

parallelogram upon the

**whole**line AB by the parallelogram CL upon the otherhalf CB : of all ...

Side 154

... BCD : as therefore BA to AE , so is BD to DC ; wherefore the rectangle BA , DC

is equal to the rectan A A gle BD , AE : but the rectangle BC , AD has been shown

equal to the rectangle BD , CE ; therefore the

... BCD : as therefore BA to AE , so is BD to DC ; wherefore the rectangle BA , DC

is equal to the rectan A A gle BD , AE : but the rectangle BC , AD has been shown

equal to the rectangle BD , CE ; therefore the

**whole**rectangle AC , BD ( 1. 2. ) ...### 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.