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 |
Inni boken
Resultat 6-10 av 59
Side 66
... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes through the centre ; and of the rest , that which is nearer to that through the centre is always greater than the more ...
... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes through the centre ; and of the rest , that which is nearer to that through the centre is always greater than the more ...
Side 69
... pass through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . Ir two circles touch each other externally , the straight line which joins their centres , shall pass through the point of contact . Let the two circles ...
... pass through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . Ir two circles touch each other externally , the straight line which joins their centres , shall pass through the point of contact . Let the two circles ...
Side 70
... passes through the point of contactd ; but it does not pass through it , because the points B , D are with- out the straight line GH , which is absurd : Therefore one circle cannot touch another on the inside in more points than one ...
... passes through the point of contactd ; but it does not pass through it , because the points B , D are with- out the straight line GH , which is absurd : Therefore one circle cannot touch another on the inside in more points than one ...
Side 71
... passing through the centre , cuts the straight line AB , which does not pass through the centre , at right angles , it also bisects it : Wherefore AF is A equal to FB , and AB double of AF . For the same reason CD is double of CG : And ...
... passing through the centre , cuts the straight line AB , which does not pass through the centre , at right angles , it also bisects it : Wherefore AF is A equal to FB , and AB double of AF . For the same reason CD is double of CG : And ...
Side 74
... passes between that straight line and , the perpendicu lar AE . And this is all that is to be understood , when , in the Greek text , and translations from it , the angle of the semicircle is said to be greater than any acute rectili ...
... passes between that straight line and , the perpendicu lar AE . And this is all that is to be understood , when , in the Greek text , and translations from it , the angle of the semicircle is said to be greater than any acute rectili ...
Andre utgaver - Vis alle
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 base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter 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 meet 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 third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 3-7 - 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 16 - Any two sides of a triangle are together greater than the third side.
Side 26 - 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 16 - 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 304 - 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 4 - 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 147 - 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 3-16 - 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 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.