## 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 |

### Inni boken

Resultat 1-5 av 15

Side 169

Wherefore , if a

angle is contained by plane angles which together are less than four right angles

. First , let the

Wherefore , if a

**solid**angle , & c . Q. E. D. B PROP . XXI . THEOR . Every**solid**angle is contained by plane angles which together are less than four right angles

. First , let the

**solid**angle at A be contained by three plane angles BAC , CAD ... Side 177

the

the figure AF with the figure KP , because they are equal and similar to one

another : therefore the straight lines AE , EF , FB , coincide with KO , OP , PL ; and

the ...

the

**solid**angle at K ; wherefore the plane AF coincides with the plane KP , andthe figure AF with the figure KP , because they are equal and similar to one

another : therefore the straight lines AE , EF , FB , coincide with KO , OP , PL ; and

the ...

Side 181

M BH , and the

sides about the equal anF gles ECG , BAK are proportionals : therefore the

parallelogram BK is simiG lar to EG . For the same reason , the parallelogram

A B C E KH ...

M BH , and the

**solid**AL : L and because , as EC to H CG , so BA to AK , the Dsides about the equal anF gles ECG , BAK are proportionals : therefore the

parallelogram BK is simiG lar to EG . For the same reason , the parallelogram

A B C E KH ...

Side 184

lelopiped ; but the

opposite parallelogram , is equal ( 29. 11. ) to the

the parallelogram ACBL , to which ORQP Ν Κ G E P м . Н Q R ' B A с is the one ...

lelopiped ; but the

**solid**CM , of which the base is ACBL , to which FDHM is theopposite parallelogram , is equal ( 29. 11. ) to the

**solid**CP , of which the base isthe parallelogram ACBL , to which ORQP Ν Κ G E P м . Н Q R ' B A с is the one ...

Side 185

the

parallelopiped CR is cut by the plane LMFD , which is parallel to the opposite

planes CP , BR ; as the base CD to the base LQ , so P F R is the

N M E

the

**solid**AE to the**solid**LR : for the same reason , because the**solid**parallelopiped CR is cut by the plane LMFD , which is parallel to the opposite

planes CP , BR ; as the base CD to the base LQ , so P F R is the

**solid**CF to theN M E

**solid**LR ...### 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.