The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Seite 4
... PROBLEM . To describe an equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe ( 3 ...
... PROBLEM . To describe an equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe ( 3 ...
Seite 10
... problem , it may be demonstrated , that two straight lines cannot have a common segment . E If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles ...
... problem , it may be demonstrated , that two straight lines cannot have a common segment . E If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles ...
Seite 136
... problem . ] 16. Similar polygons , whether inscribed in or described about circles , have their perimeters in the ratio of the diameters of those circles , and their areas in the duplicate ratio of those diameters ; and one inscribed ...
... problem . ] 16. Similar polygons , whether inscribed in or described about circles , have their perimeters in the ratio of the diameters of those circles , and their areas in the duplicate ratio of those diameters ; and one inscribed ...
Seite 139
... problem could hardly be To these may be added the inferences : -the three sides of a triangle are in one plane ; if two straight lines meet one another , they are in one plane ; and some others of like kind , which are occasionally ...
... problem could hardly be To these may be added the inferences : -the three sides of a triangle are in one plane ; if two straight lines meet one another , they are in one plane ; and some others of like kind , which are occasionally ...
Seite 140
... problems in space that are requisite as subordinate to demonstration are always given by Euclid ; and , indeed , an adherence to this practice is in some respects desirable . Those which occur are however so simple , and the processes ...
... problems in space that are requisite as subordinate to demonstration are always given by Euclid ; and , indeed , an adherence to this practice is in some respects desirable . Those which occur are however so simple , and the processes ...
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ABC is equal ABCD angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes curve described Descriptive Geometry dicular dihedral angles directrix distance draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple opposite orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane projector Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical spherical angle tangent THEOR trace triangle ABC trihedral vertex vertical plane Whence Wherefore
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Seite 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.
Seite 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.
Seite 4 - AB; but things which are equal to the same are equal to one another...
Seite 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.
Seite 8 - If two triangles have two sides of the one equal to two sides of the...
Seite 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...
Seite 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.
Seite 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.
Seite 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Seite 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.