The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
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Σελίδα 8
2. Propositions fall into two classes , problems and theorems .. 3. A Problem proposes some geometrical construction to be done -e.g. , the construction of a figure . 4. A Theorem proposes some geometrical property to be demonstrated .
2. Propositions fall into two classes , problems and theorems .. 3. A Problem proposes some geometrical construction to be done -e.g. , the construction of a figure . 4. A Theorem proposes some geometrical property to be demonstrated .
Σελίδα 9
2. Propositions fall into two classes , problems and theorems . 3. A Problem proposes some geometrical construction to be done -e.g. , the construction of a figure . 4. A Theorem proposes some geometrical property to be demonstrated .
2. Propositions fall into two classes , problems and theorems . 3. A Problem proposes some geometrical construction to be done -e.g. , the construction of a figure . 4. A Theorem proposes some geometrical property to be demonstrated .
Σελίδα 9
O Construction . From the centre A , at the distance AB , describe the circle BCD ( Postulate 3 ) ; from the centre B , at the distance BA , describe the circle ACE ; and from C , one of the points in which the circles cut one another ...
O Construction . From the centre A , at the distance AB , describe the circle BCD ( Postulate 3 ) ; from the centre B , at the distance BA , describe the circle ACE ; and from C , one of the points in which the circles cut one another ...
Σελίδα 11
D F Construction . From the point A draw the straight line AD equal to C ( I. 2 ) ; and from the centre A , at the ... But the straight line C is equal to AD ( constr . ) ; whence AE and C are each of them equal to AD ; wherefore 2.
D F Construction . From the point A draw the straight line AD equal to C ( I. 2 ) ; and from the centre A , at the ... But the straight line C is equal to AD ( constr . ) ; whence AE and C are each of them equal to AD ; wherefore 2.
Σελίδα 13
A F a E Construction . In BD take any point F ; and from AE the greater , cut off AG equal to AF the less ( I. 3 ) , and join FC , GB . Demonstration . Because AF is equal to AG ( constr . ) , and AB to AC ( hyp . ) ...
A F a E Construction . In BD take any point F ; and from AE the greater , cut off AG equal to AF the less ( I. 3 ) , and join FC , GB . Demonstration . Because AF is equal to AG ( constr . ) , and AB to AC ( hyp . ) ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal alternate angle ABC angle ACB angle BAC base base BC bisected centre circle ABC circumference common compounded constr Construction Demonstration describe diameter divided double draw equal angles equiangular equimultiples exterior angle extremities fall fore four fourth given point given straight line greater half inscribed interior join less Let ABC likewise magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular plane polygon produced Proof proportionals proved Q.E.D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square on AC straight line BC taken third touches the circle triangle ABC unequal wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 1 - 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 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Σελίδα 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Σελίδα 269 - 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 199 - 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 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 63 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Σελίδα 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
| Συγγραφέας | Euclides |
| Επιμελητής | James Martin (of the Wedgwood inst, Burslem) |
| Εκδόθηκε | 1874 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 8 Σεπτ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |