## 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 20

ABC be any triangle ; any two of A its angles together are less than two right

angles . Produce BC to D ; and because ACD is the exterior angle of the triangle

...

**THEOR**. Any two angles of a triangle are together less than two right angles . LetABC be any triangle ; any two of A its angles together are less than two right

angles . Produce BC to D ; and because ACD is the exterior angle of the triangle

...

Side 32

PROP . XXXVI .

the same parallels , are equal to one another . Let ABCD , EFGH be pa . A D H

rallelograms upon equal bases BC , FG , and between the same parallels AH ,

BG ...

PROP . XXXVI .

**THEOR**. PARALLELOGRAMS upon equal bases , and betweenthe same parallels , are equal to one another . Let ABCD , EFGH be pa . A D H

rallelograms upon equal bases BC , FG , and between the same parallels AH ,

BG ...

Side 49

acute angles to the opposite side produced , the square of the side subtending

the obtuse angle is greater than the squares of the sides containing the obtuse ...

**THEOR**. In obtuse angled triangles , if a perpendicular be drawn from any of theacute angles to the opposite side produced , the square of the side subtending

the obtuse angle is greater than the squares of the sides containing the obtuse ...

Side 56

V.

Let the two circles ABC , CDG cut one another in the points B , C ; they have not

the same centre . For , if it be possible , let E be their centre : join EC , and draw ...

V.

**THEOR**. If two circles cut one another , they shall not have the same centre .Let the two circles ABC , CDG cut one another in the points B , C ; they have not

the same centre . For , if it be possible , let E be their centre : join EC , and draw ...

Side 60

their centres being produced shall pass through the point of contact . Let the two

circles ABC , ADE touch each other internally in the point A , and let F be the

centre ...

**THEOR**. If two circles touch each other internally , the straight line which joinstheir centres being produced shall pass through the point of contact . Let the two

circles ABC , ADE touch each other internally in the point A , and let F be the

centre ...

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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.