## 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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Side 482

Whatever be the

arch , that arcb will contain the same number of degrees , minutes , seconds , & c

. as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle ...

Whatever be the

**radius**of the circle of which the mea . sure of a given angle is anarch , that arcb will contain the same number of degrees , minutes , seconds , & c

. as is manifest from Lemma 2 . III . Let AB be produced till it meet the circle ...

Side 483

4 . secanı , of any arch which is the measure of any given angle ABC , is to the

fine , versed fine , tangent , and Tecant , of any other arch which is the measure of

ilie fame angle , as the

4 . secanı , of any arch which is the measure of any given angle ABC , is to the

fine , versed fine , tangent , and Tecant , of any other arch which is the measure of

ilie fame angle , as the

**radius**of the first is to the**radius**of the second . Let AC ... Side 484

The

ABC . Since CD , AE are parallel , BD is to BC or BA , as BA to BE . PRO P. I. Fig .

5 . IN N a right angled plain triangle , if the hypothenuse be made

The

**radius**is a mean proportional between the cooline and secant of ary angleABC . Since CD , AE are parallel , BD is to BC or BA , as BA to BE . PRO P. I. Fig .

5 . IN N a right angled plain triangle , if the hypothenuse be made

**radius**, the ... Side 485

Since CEB , CDB are right angles , BC being

CBA , and BD the fine of the angle ACB ; but the iwo tri . aogles CAE , DAB bave

each a right angle at . D and E ; and likewise the common angle CAB ; therefore ...

Since CEB , CDB are right angles , BC being

**radius**, CE is the fine of the angleCBA , and BD the fine of the angle ACB ; but the iwo tri . aogles CAE , DAB bave

each a right angle at . D and E ; and likewise the common angle CAB ; therefore ...

Side 486

IN any plain triangle BAC , whose two sides are BA , AC and base BC , the less of

the two sides , which let be BA , is to the greater AC as the

of an angle ; and the

IN any plain triangle BAC , whose two sides are BA , AC and base BC , the less of

the two sides , which let be BA , is to the greater AC as the

**radius**is to the tangentof an angle ; and the

**radius**is to the tangent of the excess of this angle above ...### 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.