The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedConrad and Company, 1892 - 518 sider |
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Side 38
... 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 ...
Side 59
... 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 ...
Side 60
... half the sum of the remaining angles . The following theorems were added as corollaries to Proposition 32 by Robert Simson . COROLLARY 1. All the interior angles of any rectilineal figure , with four right angles , are together equal to ...
... half the sum of the remaining angles . The following theorems were added as corollaries to Proposition 32 by Robert Simson . COROLLARY 1. All the interior angles of any rectilineal figure , with four right angles , are together equal to ...
Side 65
... 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 ...
Side 69
... half of the parallelogram EBCA , for the diagonal AB bisects it . I. 34 . Also the triangle DBC is half of the parallelogram DBCF , I. 34 . for the diagonal DC bisects it . But the halves of equal things are equal ; Ax . 7 . therefore ...
... half of the parallelogram EBCA , for the diagonal AB bisects it . I. 34 . Also the triangle DBC is half of the parallelogram DBCF , I. 34 . for the diagonal DC bisects it . But the halves of equal things are equal ; Ax . 7 . therefore ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid exterior angle find the locus given circle given point given straight line Given the base given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY point of contact polygon produced Proof proportional PROPOSITION PROPOSITION 21 prove quadrilateral radical axis radius rect rectangle contained rectilineal figure regular polygon right angles segment shew shewn Similarly square straight line drawn tangent THEOREM triangle ABC vertex vertical angle
Populære avsnitt
Side 333 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Side 1 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 45 - 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.
Side 142 - In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Side 148 - 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.
Side 377 - 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.
Side 308 - From this it is manifest, that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Side 3 - 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.
Side 73 - 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.
Side 7 - 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.