The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick |
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Αποτελέσματα 1 - 5 από τα 96.
Σελίδα 10
to the angle EBA ; in the same manner , because ABD is a straight line , the angle
DBE is equal to the angle EBA ; wherefore ( 1 Ax . ) the angle DBE is equal to the
angle CBE , the less to the greater ; which is impossible ; therefore two straight ...
to the angle EBA ; in the same manner , because ABD is a straight line , the angle
DBE is equal to the angle EBA ; wherefore ( 1 Ax . ) the angle DBE is equal to the
angle CBE , the less to the greater ; which is impossible ; therefore two straight ...
Σελίδα 11
And , in like manner , it may he demonstrated , that no other can be in the same
straight line with it but BD , which therefore is in the same straight line with CB .
Wherefore , if at a point , etc . Q . E . D . PROPOSITION XV . Theor . If two straight
...
And , in like manner , it may he demonstrated , that no other can be in the same
straight line with it but BD , which therefore is in the same straight line with CB .
Wherefore , if at a point , etc . Q . E . D . PROPOSITION XV . Theor . If two straight
...
Σελίδα 12
Take away the common angle AED , and the remaining angle CEA is equal ( 3
Ax . ) to the remaining angle DEB . In the same manner it can be demonstrated ,
that the angles CEB , AED are equal . Therefore , if two straight lines , etc . Q . E .
D ...
Take away the common angle AED , and the remaining angle CEA is equal ( 3
Ax . ) to the remaining angle DEB . In the same manner it can be demonstrated ,
that the angles CEB , AED are equal . Therefore , if two straight lines , etc . Q . E .
D ...
Σελίδα 13
In like manner , it may be deinonstrated , that BAC , ACB , as also CAB , ABC ,
are less than two right angles . Therefore any two angles , etc . Q . E . D .
PROPOSITION XVIII . Theor . The greater side of every triangle is opposite to the
is greater ...
In like manner , it may be deinonstrated , that BAC , ACB , as also CAB , ABC ,
are less than two right angles . Therefore any two angles , etc . Q . E . D .
PROPOSITION XVIII . Theor . The greater side of every triangle is opposite to the
is greater ...
Σελίδα 14
In the same manner it may be demonstrated , that the sides AB , BC , are greater
than CA , and BC , CA greater than AB . Therefore any two sides , etc . Q . E . D .
PROPOSITION XXI . Theor . If from the ends of the side of a triangle there be ...
In the same manner it may be demonstrated , that the sides AB , BC , are greater
than CA , and BC , CA greater than AB . Therefore any two sides , etc . Q . E . D .
PROPOSITION XXI . Theor . If from the ends of the side of a triangle there be ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC axis base bisected called centre circle circumference coincide common cone construction contained coordinate planes describe diameter difference dihedral angles distance divided double draw drawn edges equal equal angles equimultiples extremities faces figure four fourth given line given point greater hence horizontal inclination intersection join less likewise magnitudes manner means meet method multiple opposite parallel parallel planes parallelogram pass perpendicular perspective picture plane MN plane of projection position preceding prism problem produced projection Prop proportionals PROPOSITION ratio reason rectangle rectilineal remaining respectively right angles segment shadow shown sides similar sphere square straight line surface taken tangent THEOR third touch trace triangle triangle ABC vertical Whence Wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 4 - AB; but things which are equal to the same are equal to one another...
Σελίδα 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Σελίδα 8 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Σελίδα 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Σελίδα 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 116 - 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.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick Τόμος 2 του An Elementary Course of Mathematics, Royal Military Academy, Woolwich |
| Συγγραφέας | Royal Military Academy, Woolwich |
| Εκδότης | J. Weale, 1853 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 14 Ιουλ. 2007 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |