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 270
Upon the square ABCD erect a prism of the same altitude with the cylinder ; this
prism is greater than half of the cylinder ; because if a square be described about
the circle , and a prism erected upon the square , of the same altitude with the ...
Upon the square ABCD erect a prism of the same altitude with the cylinder ; this
prism is greater than half of the cylinder ; because if a square be described about
the circle , and a prism erected upon the square , of the same altitude with the ...
Side 272
B. XII . above the third part of the cylinder . Let these be the ... Therefore this prism
is greater than the cylinder of which the base is the circle ABCD . B But it is also
less , for it is contained F within the cylinder ; which is impossible . Therefore the ...
B. XII . above the third part of the cylinder . Let these be the ... Therefore this prism
is greater than the cylinder of which the base is the circle ABCD . B But it is also
less , for it is contained F within the cylinder ; which is impossible . Therefore the ...
Side 280
Therefore the line GH is the circumference of a circle 1 . of which the centre is the
point K : therefore the plane GH divides the cylinder AD into the cylinders AH ,
GD ; for they are the same which would be described by the revolution of the ...
Therefore the line GH is the circumference of a circle 1 . of which the centre is the
point K : therefore the plane GH divides the cylinder AD into the cylinders AH ,
GD ; for they are the same which would be described by the revolution of the ...
Side 281
axis KL and cylinder PG ; and of the axis KF and cylinder GD , B. XII . any
equimultiples whatever , viz . the axis KM and cylinder GQ : and it has been
demonstrated , if the axis KL be greater than the axis KM , the cylinder PG is
greater than the ...
axis KL and cylinder PG ; and of the axis KF and cylinder GD , B. XII . any
equimultiples whatever , viz . the axis KM and cylinder GQ : and it has been
demonstrated , if the axis KL be greater than the axis KM , the cylinder PG is
greater than the ...
Side 282
See N. THE bases and altitudes of equal cones and cylinders are reciprocally
proportional , and , if the bases and ... through the H point P , cut the A к cylinder
EO by E M G the plane TYS parallel to the opB F posite planes of the circles
EFGH ...
See N. THE bases and altitudes of equal cones and cylinders are reciprocally
proportional , and , if the bases and ... through the H point P , cut the A к cylinder
EO by E M G the plane TYS parallel to the opB F posite planes of the circles
EFGH ...
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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 |