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 |
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Side 312
... position directly contradicts the preceding ; wherefore A is not equal to B. The demonstration of the 10th prop ... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had ...
... position directly contradicts the preceding ; wherefore A is not equal to B. The demonstration of the 10th prop ... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had ...
Side 326
... position , viz . the third of four proportionals , is equal to the fourth , if the first be equal to the second , had been given ... shown at the greater length , both because it affords a cer- tain proof of the vitiation of the text of ...
... position , viz . the third of four proportionals , is equal to the fourth , if the first be equal to the second , had been given ... shown at the greater length , both because it affords a cer- tain proof of the vitiation of the text of ...
Side 333
... position of the sides which contain the figures , to one another , depending partly upon each of these : And for the ... given no definition of equal figures , and it is certain he did not give this : For what is called the first ...
... position of the sides which contain the figures , to one another , depending partly upon each of these : And for the ... given no definition of equal figures , and it is certain he did not give this : For what is called the first ...
Side 346
... give these two cases separately : The demonstration also is made something shorter by following the way Euclid has ... position 33 . PROP . D. B. XI . It is very probable that Euclid gave this proposition a place in the Elements ...
... give these two cases separately : The demonstration also is made something shorter by following the way Euclid has ... position 33 . PROP . D. B. XI . It is very probable that Euclid gave this proposition a place in the Elements ...
Side 353
... position , something altered , and more briefly demonstrated . In the corollary of this proposition , it is supposed ... given , it was thought proper to give it , and to demonstrate that the pyramids in it . are similar to those ...
... position , something altered , and more briefly demonstrated . In the corollary of this proposition , it is supposed ... given , it was thought proper to give it , and to demonstrate that the pyramids in it . are similar to those ...
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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
ABC is given AC is equal altitude angle ABC angle BAC arch base BC bisected Book XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawa drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR triangle ABC versed sine vertex wherefore
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.