The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Σελίδα 9
... ends , such a portion is called a finite straight line . II . A terminated right line may be produced to any length in a right line . Every right line may extend without limit in either direction Воск 1. ] THE ELEMENTS OF EUCLID .
... ends , such a portion is called a finite straight line . II . A terminated right line may be produced to any length in a right line . Every right line may extend without limit in either direction Воск 1. ] THE ELEMENTS OF EUCLID .
Σελίδα 10
... produced , whenever we please , into an indefinite right line . III . A circle may be described from any centre , and with any distance from that centre as radius . B If there be two points A and B , and if with any instruments , such ...
... produced , whenever we please , into an indefinite right line . III . A circle may be described from any centre , and with any distance from that centre as radius . B If there be two points A and B , and if with any instruments , such ...
Σελίδα 15
... produced to meet the circles again in G and H , the points G , F , H are collinear , and the triangle GCH is equi ... Produce DB to meet the circle ECH in E ( Post . II . ) . With D as centre , and DE as radius , describe the circle EFG ...
... produced to meet the circles again in G and H , the points G , F , H are collinear , and the triangle GCH is equi ... Produce DB to meet the circle ECH in E ( Post . II . ) . With D as centre , and DE as radius , describe the circle EFG ...
Σελίδα 17
... produce the less of two given lines until the whole produced line becomes equal to the greater . PROP . IV . - THEOREM . If two triangles ( BAC , EDF ) have two sides ( BA , AC ) of one equal respectively to two sides ( ED , DF ) of the ...
... produce the less of two given lines until the whole produced line becomes equal to the greater . PROP . IV . - THEOREM . If two triangles ( BAC , EDF ) have two sides ( BA , AC ) of one equal respectively to two sides ( ED , DF ) of the ...
Σελίδα 19
... produced , the external angles ( DBC , ECB ) below the base shall be equal . Dem . - In BD take any point F , and from AE , tl c greater , cut off AG equal to AF [ i ] . Join BG , CF ( Post . I. ) . Because AF is equal to AG ( const ...
... produced , the external angles ( DBC , ECB ) below the base shall be equal . Dem . - In BD take any point F , and from AE , tl c greater , cut off AG equal to AF [ i ] . Join BG , CF ( Post . I. ) . Because AF is equal to AG ( const ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal AD² adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector bisects centre chord circles touch circumference circumscribed circle collinear concurrent lines const coplanar cyclic quadrilateral Dem.-Let diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle Geometry given circle given line given point greater Hence the angle hypotenuse inscribed isosceles less line AC line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped perpendicular plane points of intersection prism PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar square on AC tangent theorem triangle ABC vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Σελίδα 182 - When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Σελίδα 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 102 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 122 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Σελίδα 226 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Σελίδα 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 63 - 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.
Σελίδα 126 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Σελίδα 194 - If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.