## The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson].1814 |

### Inni boken

Resultat 1-5 av 26

Side 474

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**sine**CD , and that extremity , is called the Versed**Sine**of the arch AC , or angle ABC . VI . A straight line AE touching the circle at A , one extremity of the arch AC , and meeting the diameter BC passing through the other extremity C ... Side 475

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**sine**, versed**sine**, tangent , and se- cant , of any other arch which is the measure of the same angle , as the radius of the first is to the radius of the second . Let AC , MN be measures of the angle ABC , according to def . J. CD the ... Side 476

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**sine**and secant of any angle ABC . Since CD , AE , are parallel , BD is to BC or BA , as BA to BE . PROP . I. FIG . 5 . IN a right angled plane triangle : if the hypothe- puse be made radius , the sides become the sines of the angles ... Side 477

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**sine**of the angle CBA , and BD the**sine**of the angle ACB ; but the two triangles CAE , DAB have each a right angle at D and E ; and likewise the common angle CAB ; therefore they are similar , and consequently , CA is to AB , as CE to ... Side 479

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**sine**of BAD , which is the complement of the angle ABC ; that is , as radius to the cosine of ABC . PROP . VI . FIG . 11 .. IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half the perimeter ...### Andre utgaver - Vis alle

The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 3-7 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 16 - Any two sides of a triangle are together greater than the third side.

Side 26 - 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 16 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Side 304 - 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 4 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.

Side 147 - 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 3-16 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.