Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 páginas |
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... apply themselves to Logic without studying in some department of Mathematics ; taking noise and wrangling for proficiency , and thinking refutation accomplished by the instancing of a doubt . This will explain the inscription placed by ...
... apply themselves to Logic without studying in some department of Mathematics ; taking noise and wrangling for proficiency , and thinking refutation accomplished by the instancing of a doubt . This will explain the inscription placed by ...
Página 37
... apply a parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . Let AB be the given straight line , and C the given triangle , and D the given rectilineal angle . It is ...
... apply a parallelogram , which shall be equal to a given triangle , and have one of its angles equal to a given rectilineal angle . Let AB be the given straight line , and C the given triangle , and D the given rectilineal angle . It is ...
Página 38
... apply the parallelogram GM equal to the triangle DBC , having the angle GHM equal to the angle E. ( 1. 44. ) Then the figure FKML shall be the parallelogram required . Because each of the angles FKH , GHM , is equal to the angle E ...
... apply the parallelogram GM equal to the triangle DBC , having the angle GHM equal to the angle E. ( 1. 44. ) Then the figure FKML shall be the parallelogram required . Because each of the angles FKH , GHM , is equal to the angle E ...
Página 39
... apply a parallelogram , which shall have an angle equal to a given rectilineal angle , and shall be equal to a given rectilineal figure ; viz . by applying to the given straight line a parallelogram equal to the first triangle ABD , ( 1 ...
... apply a parallelogram , which shall have an angle equal to a given rectilineal angle , and shall be equal to a given rectilineal figure ; viz . by applying to the given straight line a parallelogram equal to the first triangle ABD , ( 1 ...
Página 43
... apply to every direction on every side of the line between its extremities . Every straight line situated in a plane , is considered to have two sides ; and when the direction of a line is known , the line is said to be given in ...
... apply to every direction on every side of the line between its extremities . Every straight line situated in a plane , is considered to have two sides ; and when the direction of a line is known , the line is said to be given in ...
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Términos y frases comunes
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
Pasajes populares
Página 54 - If two triangles have two sides of the one equal to two sides of the...
Página 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...
Página 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.
Página 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.
Página 18 - Any two angles of a triangle are together less than two right angles.
Página 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.
Página 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.
Página 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.
Página 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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...