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 37
... angle D. Which was to be done . PROP . XLIII . THEOR . THE complements of the parallelograms , which are about the ... remaining complement BK is equal to the remaining complement KD . Wherefore the complements , & c . Q. E. D. ...
... angle D. Which was to be done . PROP . XLIII . THEOR . THE complements of the parallelograms , which are about the ... remaining complement BK is equal to the remaining complement KD . Wherefore the complements , & c . Q. E. D. ...
Side 51
... angle ; and therefore the G F whole AEB is a right angle : And because the angle GEF is half a right angle , and EGF a CDB right angle , for it is equale to the interior and opposite an- 29. 1 . gle ECB , the remaining angle EFG is half a ...
... angle ; and therefore the G F whole AEB is a right angle : And because the angle GEF is half a right angle , and EGF a CDB right angle , for it is equale to the interior and opposite an- 29. 1 . gle ECB , the remaining angle EFG is half a ...
Side 53
... angle : And be- cause EBC is half a right angle , DBG is alsof half a right £ 15.1 . angle , for they are vertically opposite ; but BDG is a right angle , because it is equal to the alternate angle DCE ; 29.1 . therefore the remaining angle ...
... angle : And be- cause EBC is half a right angle , DBG is alsof half a right £ 15.1 . angle , for they are vertically opposite ; but BDG is a right angle , because it is equal to the alternate angle DCE ; 29.1 . therefore the remaining angle ...
Side 54
... angle EAB is a right angle ; therefore the rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE : Take A away the square of AE , which is com- mon to both , therefore the remaining rectangle CF , FA ...
... angle EAB is a right angle ; therefore the rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE : Take A away the square of AE , which is com- mon to both , therefore the remaining rectangle CF , FA ...
Side 67
... angle EMD is greater than the angle FMD ; therefore the base ED is greater than the base FD . like manner it may be ... remain- C der KD is greater d than the re- mainder GD , that is GD is less M 4 Ax . than KD : And because MK ...
... angle EMD is greater than the angle FMD ; therefore the base ED is greater than the base FD . like manner it may be ... remain- C der KD is greater d than the re- mainder GD , that is GD is less M 4 Ax . than KD : And because MK ...
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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.