The Elements of Euclid, books i. to vi., with deductions, appendices and historical notes, by J.S. Mackay. [With] Key1884 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 18
... converse of a theorem is derived from the theorem by inter- changing the hypothesis and the conclusion . Thus , the converse of the theorem mentioned above is , ' If in a triangle the angles opposite two sides be equal , the sides shall ...
... converse of a theorem is derived from the theorem by inter- changing the hypothesis and the conclusion . Thus , the converse of the theorem mentioned above is , ' If in a triangle the angles opposite two sides be equal , the sides shall ...
Σελίδα 67
... converse of I. 17. ] I. 17 I. 13 Hyp . 1. In the diagram to I. 28 , if AB is || CD , prove AGE = 2 DHF , and BGE + L DHF = 2 rt . 4 s . 2. If a straight line be perpendicular to one of two parallels , it is also perpendicular to the ...
... converse of I. 17. ] I. 17 I. 13 Hyp . 1. In the diagram to I. 28 , if AB is || CD , prove AGE = 2 DHF , and BGE + L DHF = 2 rt . 4 s . 2. If a straight line be perpendicular to one of two parallels , it is also perpendicular to the ...
Σελίδα 73
... converse of this proposition . I. 27 2. If a quadrilateral have one pair of opposite sides equal and parallel , it is a || m . 3. What statements may be made about the straight lines which join the ends of two equal and parallel ...
... converse of this proposition . I. 27 2. If a quadrilateral have one pair of opposite sides equal and parallel , it is a || m . 3. What statements may be made about the straight lines which join the ends of two equal and parallel ...
Σελίδα 77
... converse of the last deduction . 6. Equal || ms situated between the same parallels have equal bases . PROPOSITION 37 . THEOREM . Triangles on the same base and between the same parallels are equal in area . A D B Let ABC , DBC be ...
... converse of the last deduction . 6. Equal || ms situated between the same parallels have equal bases . PROPOSITION 37 . THEOREM . Triangles on the same base and between the same parallels are equal in area . A D B Let ABC , DBC be ...
Σελίδα 80
... converse of the last deduction . 3. Two triangles are between the same parallels , and the base of the first is double the base of the second ; prove the first triangle double the second . 4. The four triangles into which the diagonals ...
... converse of the last deduction . 3. Two triangles are between the same parallels , and the base of the first is double the base of the second ; prove the first triangle double the second . 4. The four triangles into which the diagonals ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid, books i. to vi., with deductions, appendices and ... Euclides Πλήρης προβολή - 1885 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon Mackay,John Sturgeon Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon MacKay,John Sturgeon Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² AD² angles equal base BC bisected bisector CD² centre chord circumscribed Const deduction diagonals diameter divided in medial divided internally draw equiangular equilateral triangle equimultiples Euclid's exterior angles Find the locus given circle given point given straight line greater Hence hypotenuse inscribed intersection isosceles triangle less Let ABC lines is equal magnitudes medial section median meet middle points opposite sides orthocentre parallel parallelogram perpendicular polygon produced PROPOSITION 13 Prove the proposition quadrilateral radical axis radii radius ratio rectangle contained rectilineal figure regular pentagon required to prove rhombus right angle right-angled triangle square on half straight line drawn straight line joining tangent THEOREM unequal segments vertex vertical angle Нур
Δημοφιλή αποσπάσματα
Σελίδα 147 - 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.
Σελίδα 276 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words
Σελίδα 331 - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Σελίδα 17 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Σελίδα 112 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 87 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Σελίδα 254 - If there be four magnitudes, and if any equimultiples whatsoever be taken of the first and third, and any equimultiples whatsoever of the second and fourth, and if, according as the multiple of the first is greater than the multiple of the second, equal to it or less, the multiple of the third is also greater than the multiple of the fourth, equal to it or less ; then, the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth.
Σελίδα 138 - RULE. from half the sum of the three sides, subtract each side separately; multiply the half sum and the three remainders together, and the square root of the product will be the area required.
Σελίδα 304 - 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.
Σελίδα 44 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.