## The Elements of Euclid, Viz: 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. the first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 85

Side 6

Now , this Propofition is a Theorem , not a Definition ; because the equality of

Figures of any kind

though this were a true Propofition , it ought to have been demonstrated . But

indeed ...

Now , this Propofition is a Theorem , not a Definition ; because the equality of

Figures of any kind

**must**be demonstrated , and not affumed ; and , therefore ,though this were a true Propofition , it ought to have been demonstrated . But

indeed ...

Side 29

O make a triangle of which the sides shall be equal SceN ! to three given ftraight

lines ; but any two whatever of these

be the three given straight lines , of which any two whatever are greater than ...

O make a triangle of which the sides shall be equal SceN ! to three given ftraight

lines ; but any two whatever of these

**must**be greater than the third a . Let A , B , Cbe the three given straight lines , of which any two whatever are greater than ...

Side 32

I. For , if it be not greater , it

is not equal to the angle EPF , because then the base BC would be equal · A to

EF ; but it is not ; therefore the angle BAC is not equal to the angle EDF ; neither

is ...

I. For , if it be not greater , it

**must**either be equal to it , or lefs ; but the angle BACis not equal to the angle EPF , because then the base BC would be equal · A to

EF ; but it is not ; therefore the angle BAC is not equal to the angle EDF ; neither

is ...

Side 35

A B For , if AGH be not equal to GHD , one of them

; let AGH be the greater ; and С H D because the angle AGH is greater F than the

angle GHD , add to each of them the angle BGH ; therefore the angles AGH ...

A B For , if AGH be not equal to GHD , one of them

**must**be greater than the other; let AGH be the greater ; and С H D because the angle AGH is greater F than the

angle GHD , add to each of them the angle BGH ; therefore the angles AGH ...

Side 67

This is not a definition but a theorem , the truth of which is evident ; for , if the

circles be applied to one another , so that their centers coincide , the circles

likewise coincide , fince the straight lines from their centers are equal . ' II . A

straight ...

This is not a definition but a theorem , the truth of which is evident ; for , if the

circles be applied to one another , so that their centers coincide , the circles

**must**likewise coincide , fince the straight lines from their centers are equal . ' II . A

straight ...

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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 32 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.

Side 170 - 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 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...

Side 55 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

Side 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.

Side 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.