Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Αποτελέσματα 1 - 5 από τα 38.
Σελίδα 57
... segment BD . PROP . XIII . THEOR . In any triangle ( ABC ) the square of a side ( CB ) subtending an acute angle , is less than the sum of the squares of the sides ( CA , AB ) containing that angle , by twice the rectangle contained by ...
... segment BD . PROP . XIII . THEOR . In any triangle ( ABC ) the square of a side ( CB ) subtending an acute angle , is less than the sum of the squares of the sides ( CA , AB ) containing that angle , by twice the rectangle contained by ...
Σελίδα 58
... segment adjacent to the acute angle . Next , suppose that the perpendicular CD falls outside of the triangle ABC . Then AD2 + AB2 = 2 AD'AB + BD2 ( ii . Prop . 7 ) ; add to both DC2 , and then DC2 + AD2 + AB2 = 2 AD AB + BD2 + DC2 ; but ...
... segment adjacent to the acute angle . Next , suppose that the perpendicular CD falls outside of the triangle ABC . Then AD2 + AB2 = 2 AD'AB + BD2 ( ii . Prop . 7 ) ; add to both DC2 , and then DC2 + AD2 + AB2 = 2 AD AB + BD2 + DC2 ; but ...
Σελίδα 59
... SEGMENT of a circle is the figure contained by a straight line , and the arch which it cuts off . 1D 9. An angle in a segment is the angle made [59] ...
... SEGMENT of a circle is the figure contained by a straight line , and the arch which it cuts off . 1D 9. An angle in a segment is the angle made [59] ...
Σελίδα 60
... segment . 10. An angle in a segment is said to stand upon the arch intercepted between the straight lines which make the angle . 11. A SECTOR of a circle is the figure contained by two rays and the arch between them . 12. Similar ...
... segment . 10. An angle in a segment is said to stand upon the arch intercepted between the straight lines which make the angle . 11. A SECTOR of a circle is the figure contained by two rays and the arch between them . 12. Similar ...
Σελίδα 64
... segment of AL , which is con- sequently itself equal to AE . Also , any other line drawn from the point A to the circumference , must either pass through the centre , and consequently be greater than AE or AL , or else it must lie at ...
... segment of AL , which is con- sequently itself equal to AE . Also , any other line drawn from the point A to the circumference , must either pass through the centre , and consequently be greater than AE or AL , or else it must lie at ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ACDB adjacent angles angles equal antecedent Axioms base bisected centre chord circumference coincide consequently Const definition demonstrated describe diagonal diameter difference divided draw equal angles equal Prop equal sides equiangular equilateral triangle equimultiples Euclid Euclid's Elements external angle extremities fore fourth fractional Geometry given angle given circle given line given point given straight line given triangle greater hypotenuse inscribed internal intersect isosceles triangle less line drawn lines be drawn magnitudes manner meeting multiple opposite angles parallel parallelogram perpendicular point of contact PROB produced proportional Proposition quadrilateral figure rectangle contained rectilinear figure remaining angles respectively equal right angle segment semiperimeter sides AC sides equal square of half subtending taken tangent THEOR third triangles ABC unequal vertex whole line
Δημοφιλή αποσπάσματα
Σελίδα 126 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 155 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 83 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 90 - BFE : (i. def. 10.) therefore, in the two triangles, EAF, EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (i.
Σελίδα 117 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Σελίδα 56 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 60 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 78 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.