The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |
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Side 87
UPON the same straight line , and upon the same see N. side of it , there cannot
be two similar segments of circles not ... DA : and because A B the segment ACB
is similar to the segment ADB , and that similar segments of circles contain b ...
UPON the same straight line , and upon the same see N. side of it , there cannot
be two similar segments of circles not ... DA : and because A B the segment ACB
is similar to the segment ADB , and that similar segments of circles contain b ...
Side 88
Book III . because AB is equal to CD : therefore , the straight line AB coinciding
with CD , the segment AEB must a coincide with the a 23. 3. segment CFD , and
therefore is equal to it . Wherefore , similar segments , & c . Q. E. D. PROP . XXV .
Book III . because AB is equal to CD : therefore , the straight line AB coinciding
with CD , the segment AEB must a coincide with the a 23. 3. segment CFD , and
therefore is equal to it . Wherefore , similar segments , & c . Q. E. D. PROP . XXV .
Side 89
From the centre E , at the distance of a any of the three AE , EB , EC , describe a
circle ; this shall pass d 9.3 . through the other points ; and the circle of which
ABC is a segment is described : and it is evident , that if the angle ABD be greater
...
From the centre E , at the distance of a any of the three AE , EB , EC , describe a
circle ; this shall pass d 9.3 . through the other points ; and the circle of which
ABC is a segment is described : and it is evident , that if the angle ABD be greater
...
Side 93
IN a circle , the angle in a semicircle is a right angle ; but the angle in a segment
greater than a semicircle is less than a ... Let ABCD be a circle , of which the
diameter is BC , and centre E ; and draw CA dividing the circle into the segments
...
IN a circle , the angle in a semicircle is a right angle ; but the angle in a segment
greater than a semicircle is less than a ... Let ABCD be a circle , of which the
diameter is BC , and centre E ; and draw CA dividing the circle into the segments
...
Side 96
3 . angle DAB is equal to the F angle in the alternate segment B g 32. 3. AHB 8 :
but the angle DAB is equal to the angle C , therefore G also the angle C is equal
to the E angle in the segment AHB : D wherefore , upon the given straight line AB
...
3 . angle DAB is equal to the F angle in the alternate segment B g 32. 3. AHB 8 :
but the angle DAB is equal to the angle C , therefore G also the angle C is equal
to the E angle in the segment AHB : D wherefore , upon the given straight line AB
...
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 30 - Any two sides of a triangle are together greater than the third side.
Side 64 - 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 30 - 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 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Side 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
| Forfatter | Robert Simson |
| Utgiver | Mathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 518 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |