## 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 100

Side 18

Because AF is equal to AG , and AB to AC ; the two sides FA , AC are equal to the

two GA , AB , each to each ; and they contain the angle FAG

triangles AFC , A AGB ; therefore the base FC is eb . 4. I. qual to the base GB ...

Because AF is equal to AG , and AB to AC ; the two sides FA , AC are equal to the

two GA , AB , each to each ; and they contain the angle FAG

**common**to the twotriangles AFC , A AGB ; therefore the base FC is eb . 4. I. qual to the base GB ...

Side 19

... and EC

each to each ; and the angle DBC is equal to the angle ACB ; therefore the bale

DC is equal to the base AB , and the triangle DBC is equal to the triangle b ACB ...

... and EC

**common**to D both , the two fides DB , BC are equal to the two AC , CB ,each to each ; and the angle DBC is equal to the angle ACB ; therefore the bale

DC is equal to the base AB , and the triangle DBC is equal to the triangle b ACB ...

Side 22

Book I. C Because AC is equal to CB , and CD

BCD ; the two fides AC , CD are equal to BC , CD , each to each ; and the angle

ACD is equal to the angle BCD ; therefore the base AD is equal to the base ...

Book I. C Because AC is equal to CB , and CD

**common**to the two triangles ACD ,BCD ; the two fides AC , CD are equal to BC , CD , each to each ; and the angle

ACD is equal to the angle BCD ; therefore the base AD is equal to the base ...

Side 23

Because FH is equal to HG , and HC

the two sides FH , HC are equal to the two GH , HC , each to each ; and the base

CF is equal to the d 55. Def . base CG ; therefore the angle CHF is equal to the ...

Because FH is equal to HG , and HC

**common**to the two triangles FHC , GHC ,the two sides FH , HC are equal to the two GH , HC , each to each ; and the base

CF is equal to the d 55. Def . base CG ; therefore the angle CHF is equal to the ...

Side 25

1 . right angles ; but the angles ABC , ABD are likewise together equal to two right

angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD :

Take away the

1 . right angles ; but the angles ABC , ABD are likewise together equal to two right

angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD :

Take away the

**common**angle ABC , the remaining angle ABE is equal to the ...### Hva folk mener - Skriv en omtale

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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

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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.