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 254
Book XII . so are the two prisms in the pyramid ABCG to the two prisms in the
pyramid DEFH ; and so are the two prisms in ... may be shown of tbe prisms
made by dividing the pyramids AKLO and DPRS , and of all made by the same
number of ...
Book XII . so are the two prisms in the pyramid ABCG to the two prisms in the
pyramid DEFH ; and so are the two prisms in ... may be shown of tbe prisms
made by dividing the pyramids AKLO and DPRS , and of all made by the same
number of ...
Side 255
ABC is not to the base DEF , as the pyramid ABCG to any solid which is less than
the pyramid DEFH . In the same manner it may be demonstrated , that the base
DEF is not to the base ABC , as the pyramid DEFH to any solid which is less than
...
ABC is not to the base DEF , as the pyramid ABCG to any solid which is less than
the pyramid DEFH . In the same manner it may be demonstrated , that the base
DEF is not to the base ABC , as the pyramid DEFH to any solid which is less than
...
Side 256
See N . PYRAMIDS of the same altitude which have polygons for their bases , are
to one another as their bases . ... N , be of the same altitude : As the base ABCDE
to the base FGHKL , so is the pyramid ABCDEM to the pyra . mid FGHKLN .
See N . PYRAMIDS of the same altitude which have polygons for their bases , are
to one another as their bases . ... N , be of the same altitude : As the base ABCDE
to the base FGHKL , so is the pyramid ABCDEM to the pyra . mid FGHKLN .
Side 257
ABCDE to the base FGHKL , so the pyramid ABCDEM to De 22 . 5 . the pyramid
FGHKLN . Therefore pyramids , & c , Q . E . D . er . PROP . VII . THEOR . Every
prism having a triangular base may be divided into three pyramids that have ...
ABCDE to the base FGHKL , so the pyramid ABCDEM to De 22 . 5 . the pyramid
FGHKLN . Therefore pyramids , & c , Q . E . D . er . PROP . VII . THEOR . Every
prism having a triangular base may be divided into three pyramids that have ...
Side 351
6 . the pyramids which have the triangles EAB , LFG , for their bases , and the
points M , N for their vertices , are ... 11 . the solids themselves are contained by
the same number of• . similar planes : In the same manner the pyramid EBCM
may ...
6 . the pyramids which have the triangles EAB , LFG , for their bases , and the
points M , N for their vertices , are ... 11 . the solids themselves are contained by
the same number of• . similar planes : In the same manner the pyramid EBCM
may ...
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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 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 figure 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 306 - 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.
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 |