Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 σελίδες |
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Σελίδα 2
... perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that ...
... perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that ...
Σελίδα 15
... perpendicular to AB from the point C. F E H B G D Upon the other side of AB take any point D , and from the center C , at the distance CD , describe the circle EGF meeting AB , produced if necessary , in Fand G : ( post . 3. ) bisect FG ...
... perpendicular to AB from the point C. F E H B G D Upon the other side of AB take any point D , and from the center C , at the distance CD , describe the circle EGF meeting AB , produced if necessary , in Fand G : ( post . 3. ) bisect FG ...
Σελίδα 44
... perpendicular to another line , the latter is also perpendicular to the former ; and always calls a right angle , ¿ půǹ γωνία ; but a straight line , εὐθεῖα γραμμή . Def . XIX . This has been restored from Proclus , as it seems to have ...
... perpendicular to another line , the latter is also perpendicular to the former ; and always calls a right angle , ¿ půǹ γωνία ; but a straight line , εὐθεῖα γραμμή . Def . XIX . This has been restored from Proclus , as it seems to have ...
Σελίδα 53
... perpendicular can be drawn from a given point to a given line ; and this perpendicular may be shewn to be less than any other line which can be drawn from the given point to the given line : and of the rest , the line which is nearer to ...
... perpendicular can be drawn from a given point to a given line ; and this perpendicular may be shewn to be less than any other line which can be drawn from the given point to the given line : and of the rest , the line which is nearer to ...
Σελίδα 58
... perpendicular , according to their position . In the diagram the three squares are described on the outer sides of the triangle ABC . The Proposition may also be demonstrated ( 1 ) when the three squares are described upon the inner ...
... perpendicular , according to their position . In the diagram the three squares are described on the outer sides of the triangle ABC . The Proposition may also be demonstrated ( 1 ) when the three squares are described upon the inner ...
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A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 89 - 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, together with the square...
Σελίδα 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Σελίδα 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 18 - Any two angles of a triangle are together less than two right angles.
Σελίδα 266 - 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.
Σελίδα 152 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...