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 8
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . D 2.1 . From the point A drawa the C straight line AD equal to C ; and ...
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . D 2.1 . From the point A drawa the C straight line AD equal to C ; and ...
Side 11
... 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 AС , СВ A each to each ; and the angle DBC is D equal to the angle ACB ...
... 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 AС , СВ A each to each ; and the angle DBC is D equal to the angle ACB ...
Side 19
... less than two right angles . In like man- ner , 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 ...
... less than two right angles . In like man- ner , 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 ...
Side 20
... less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD , be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
... less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD , be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
Side 24
... less ; because then the base BC 24. 1. would be less than D the base EF ; but it is B C E F not ; therefore the angle BAC is not less than the angle EDF ; and it was shown that it is not equal to it ; there- fore the angle BAC is ...
... less ; because then the base BC 24. 1. would be less than D the base EF ; but it is B C E F not ; therefore the angle BAC is not less than the angle EDF ; and it was shown that it is not equal to it ; there- fore the angle BAC is ...
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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.