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
In like manner , in the demonstration of the 26th Prop . of the 11th Book , it is taken for granted , that those solid angles are equal to one another which are contained by plane angles of the same number and magnitude placed in the ...
In like manner , in the demonstration of the 26th Prop . of the 11th Book , it is taken for granted , that those solid angles are equal to one another which are contained by plane angles of the same number and magnitude placed in the ...
Side 17
And , in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB .
And , in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB .
Side 35
In the same manner , it can be demonstrated , that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. È.D. PROP . XL . THEOR . Equal triangles upon equal bases , in the ...
In the same manner , it can be demonstrated , that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. È.D. PROP . XL . THEOR . Equal triangles upon equal bases , in the ...
Side 61
In the same manner it can be shown , that no other point but F is the centre ; that is , F is the centre of the circle ABC : Which was to be found . Cor . From this it is manifest , that if in a circle a straight line bisect another at ...
In the same manner it can be shown , that no other point but F is the centre ; that is , F is the centre of the circle ABC : Which was to be found . Cor . From this it is manifest , that if in a circle a straight line bisect another at ...
Side 62
In the same manner , it may be demonstrated that it does not fall upon the circumference ; it falls therefore within it , Wherefore , if any two points , & c . Q.E.D. PROP . III . THEOR . * 1. 3 . If a straight line drawn through the ...
In the same manner , it may be demonstrated that it does not fall upon the circumference ; it falls therefore within it , Wherefore , if any two points , & c . Q.E.D. PROP . III . THEOR . * 1. 3 . If a straight line drawn through the ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC arch base Book 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 45 - 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 312 - 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 155 - 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 54 - 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 167 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | 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]. |
| Forfatter | Euclides |
| Redaktør | Robert Simson |
| Utgave | 16 |
| distribuert | 1814 |
| Original fra | Oxford University |
| Digitalisert | 19. apr 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |