A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI, Libro 1Macmillan, 1900 - 456 páginas |
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Página 44
... half its perimeter . 10. The perimeter of a quadrilateral is greater than the sum of its diagonals . 11. Obtain a proof of Proposition 20 by bisecting an angle by a straight line which meets the opposite side . ON PROPOSITION 21 . 12 ...
... half its perimeter . 10. The perimeter of a quadrilateral is greater than the sum of its diagonals . 11. Obtain a proof of Proposition 20 by bisecting an angle by a straight line which meets the opposite side . ON PROPOSITION 21 . 12 ...
Página 65
... half a right angle . 4. If one angle of a triangle is equal to the sum of the other two , the triangle is right - angled . 5. The sum of the angles of any quadrilateral figure is equal to four right angles . 6. Each angle of an ...
... half a right angle . 4. If one angle of a triangle is equal to the sum of the other two , the triangle is right - angled . 5. The sum of the angles of any quadrilateral figure is equal to four right angles . 6. Each angle of an ...
Página 66
... half the sum of the remaining angles . The following theorems were added as corollaries to Proposition 32 by Robert Simson , who edited Euclid's text in 1756 . COROLLARY 1. All the interior angles of any rectilineal figure , together ...
... half the sum of the remaining angles . The following theorems were added as corollaries to Proposition 32 by Robert Simson , who edited Euclid's text in 1756 . COROLLARY 1. All the interior angles of any rectilineal figure , together ...
Página 71
... half the sum of the base angles . 7. The angle contained by the bisectors of two exterior angles of any triangle is equal to half the sum of the two corresponding interior angles . 8. If perpendiculars are drawn to two intersecting ...
... half the sum of the base angles . 7. The angle contained by the bisectors of two exterior angles of any triangle is equal to half the sum of the two corresponding interior angles . 8. If perpendiculars are drawn to two intersecting ...
Página 75
... half the parallelogram EBCA . And the diagonal DC bisects DBCF ; I. 34 . .. the triangle DBC is half the parallelogram DBCF . And the halves of equal things are equal . Ax . 7 . Therefore the triangle ABC is equal to the triangle DBC ...
... half the parallelogram EBCA . And the diagonal DC bisects DBCF ; I. 34 . .. the triangle DBC is half the parallelogram DBCF . And the halves of equal things are equal . Ax . 7 . Therefore the triangle ABC is equal to the triangle DBC ...
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Términos y frases comunes
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisected bisectors centre chord circles intersect circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter draw escribed circle Euclid's exterior angle find the locus given circle given point given straight line Given the base given triangle greater Hence hypotenuse inscribed isosceles triangle Let ABC line which joins meet middle point nine-points circle opposite angle opposite sides orthocentre par¹ parallelogram pedal triangle perp perpendiculars drawn point of contact polygon produced Proof PROPOSITION PROPOSITION 21 prove quadrilateral radical axis radius rectangle contained regular polygon rhombus right angles segment shew shewn side BC square straight line drawn subtended tangent THEOREM touch a given triangle ABC twice the rect vertex vertical angle
Pasajes populares
Página 42 - Any two sides of a triangle are together greater than the third side.
Página 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 162 - 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 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 65 - 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.
Página 68 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Página 143 - If 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.
Página 8 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Página 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Página 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.