## 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]. |

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Side 8

Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the

Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the

**less**. Side 11

1 . off DB equal to AC , the

1 . off DB equal to AC , the

**less**, and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both the two sides , DB , BC are equal to the two AC , CB each to each ; and the angle DBC is equal ... Side 19

In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are

In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are

**less**than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the ... Side 20

BOOK I. angle ABC would be

BOOK I. angle ABC would be

**less**than the angle ACB ; but it is not ; therefore the side AC is not**less**than AB ; and it has been shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Side 24

For , if it be not greater , it must either be equal to it , or

For , if it be not greater , it must either be equal to it , or

**less**; but the angle BAC is not equal to the angle EDF , because then the base 4. 1. BC would be equala A to EF : but it is not ; therefore the angle BAC is not equal to ...### Hva folk mener - Skriv en omtale

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

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added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC Take taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 43 - 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 20 - Any two sides of a triangle are together greater than the third side.

Side 30 - 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 20 - 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 310 - 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 8 - 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 153 - 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 52 - 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 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Side 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.