The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Página 6
... right angle . 12. An acute angle is that which is less than a right angle . Thus the angles ABC , ABD are each of them right angles ; EBC is an obtuse , and EBD an acute angle ; and the line AB is a perpendicular to CD . C A E D 13. " A ...
... right angle . 12. An acute angle is that which is less than a right angle . Thus the angles ABC , ABD are each of them right angles ; EBC is an obtuse , and EBD an acute angle ; and the line AB is a perpendicular to CD . C A E D 13. " A ...
Página 7
... angle GEB is equal to the angle AEG . Each is therefore a right angle . Angles are said to be of as many degrees as the arcs upon which they stand ; and it is clear that , whatever the radius of the circle , the incli- nation of an angle ...
... angle GEB is equal to the angle AEG . Each is therefore a right angle . Angles are said to be of as many degrees as the arcs upon which they stand ; and it is clear that , whatever the radius of the circle , the incli- nation of an angle ...
Página 8
... right - angled triangle is that which has a right angle . 27. An obtuse - angled triangle is that which has an obtuse angle . 28. An acute - angled triangle is that which has three acute angles . 29. Of four - sided figures , a square ...
... right - angled triangle is that which has a right angle . 27. An obtuse - angled triangle is that which has an obtuse angle . 28. An acute - angled triangle is that which has three acute angles . 29. Of four - sided figures , a square ...
Página 9
... angles are not right angles . 32. A rhomboid is that which has its opposite sides equal to one another , but all its sides are not equal , nor its angles right angles . These last four figures come also under the more ge- neral ...
... angles are not right angles . 32. A rhomboid is that which has its opposite sides equal to one another , but all its sides are not equal , nor its angles right angles . These last four figures come also under the more ge- neral ...
Página 10
... right angles are equal to one another . ( See Definition 10. ) 12. If a straight line meets two straight lines , 10 EUCLID.- -BOOK I.
... right angles are equal to one another . ( See Definition 10. ) 12. If a straight line meets two straight lines , 10 EUCLID.- -BOOK I.
Términos y frases comunes
ABCD adjacent angle contained base BC bisect CD Prop coincide Const CONST.-In CONST.-Join CONST.-Let DEMONST.-Because DEMONST.-For demonstration diam diameter draw EBCF ENUN ENUN.-If ENUN.-Let ABC ENUN.-To ENUN.-To describe equal sides equilateral Euclid EUCLID'S ELEMENTS exterior four rt given point given straight line interior and opposite interior opposite isosceles join Let ABC line be drawn line drawn meet opposite angles opposite sides parallel parallelogram perpendicular Post PROB produced Proposition proved rectilineal figure rhombus right angles side BC square take any pt THEOR THEOR.-If Theorem trapezium trapezium ABCD vertical Wherefore XXIX XXXI XXXII XXXIV XXXVIII
Pasajes populares
Página 58 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 24 - Upon the same base, and on the same side of it, there cannot be two triangles, that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity, equal to one another.
Página 34 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 6 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Página 109 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.
Página 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Página 99 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 49 - 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...
Página 104 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 6 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.