## 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 |

### Inni boken

Resultat 6-10 av 98

Side 86

... semi- D circle; and the angles in it BAC, BEC are equal, by the first

the same reason, because CBED is greater than a semicircle, the angles CAD,

CED are equal: Therefore the whole angle BAD is equal to the C whole angle

BED.

... semi- D circle; and the angles in it BAC, BEC are equal, by the first

**case**: Forthe same reason, because CBED is greater than a semicircle, the angles CAD,

CED are equal: Therefore the whole angle BAD is equal to the C whole angle

BED.

Side 127

... D : And in the same way the other

I one magnitude be the same multiple of another, so N. ! which a magnitude

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

the ...

... D : And in the same way the other

**case**is demonstrated. P R O P. V. T H E O R.I one magnitude be the same multiple of another, so N. ! which a magnitude

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

the ...

Side 130

Next, Let the first A be the same part of the second B, that the third C is of the

fourth D : A is to B, as C is to D : For B is the same multiple of A, that D is of C ;

wherefore, by the preceeding

A is ...

Next, Let the first A be the same part of the second B, that the third C is of the

fourth D : A is to B, as C is to D : For B is the same multiple of A, that D is of C ;

wherefore, by the preceeding

**case**, B is to A, as D is to C ; and in- | # i o i versely “A is ...

Side 131

... therefore B is a multiple of A; and, by the preceeding

multiple of C, that is, C is the same part of D, that A is of B: Therefore, if the first,

&c. Q. E. D. . C R - P R O P. VII. T H E O R. EQA. magnitudes have the same ratio

to the ...

... therefore B is a multiple of A; and, by the preceeding

**case**, D is the samemultiple of C, that is, C is the same part of D, that A is of B: Therefore, if the first,

&c. Q. E. D. . C R - P R O P. VII. T H E O R. EQA. magnitudes have the same ratio

to the ...

Side 132

... ther be multiplied as often ; and let EF be the multiple thus taken of AC, and FG

the same multiple of CB: Therefore {} and FG are each of thein greater than . . . .

D: And in every one of the

... ther be multiplied as often ; and let EF be the multiple thus taken of AC, and FG

the same multiple of CB: Therefore {} and FG are each of thein greater than . . . .

D: And in every one of the

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### Andre utgaver - Vis alle

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

added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder definition demonſtrated deſcribed diameter divided double draw drawn equal equiangular equimultiples exceſs fides figure firſt fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet muſt oppoſite P R O parallel parallelogram perpendicular plane produced prop proportionals propoſition pyramid reëtangle contained reëtilineal remaining right angles ſame ſame multiple ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſolid angle ſphere ſquare ſquare of AC T H E O Take taken theſe third triangle ABC wherefore whole

### 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.