Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 53
... square upon a given finite straight line . Let AB be the given straight line ; it is required to describe a square upon AB . # 11 . 1 . * 3 . 1 . * 31 . 1 . + Def . 34. 1 . From the point A draw * AC at right angles to AB ; and make ...
... square upon a given finite straight line . Let AB be the given straight line ; it is required to describe a square upon AB . # 11 . 1 . * 3 . 1 . * 31 . 1 . + Def . 34. 1 . From the point A draw * AC at right angles to AB ; and make ...
Σελίδα 54
... square described upon the side BC shall be equal to the squares described upon BA , AC . # 31 . 1 . + Hyp . On BC describe the square BDEC , and on BA , # 46 . 1. AC the squares GB , HC ; and through A draw AL parallel to BD , or CE ...
... square described upon the side BC shall be equal to the squares described upon BA , AC . # 31 . 1 . + Hyp . On BC describe the square BDEC , and on BA , # 46 . 1. AC the squares GB , HC ; and through A draw AL parallel to BD , or CE ...
Σελίδα 55
... AL ; and the square GB is double of the triangle FBC , because these also are upon the same base FB , and between the same parallels FB , GC : but the doubles of equals are equal * to # 6 Ax . one another ; therefore the parallelogram ...
... AL ; and the square GB is double of the triangle FBC , because these also are upon the same base FB , and between the same parallels FB , GC : but the doubles of equals are equal * to # 6 Ax . one another ; therefore the parallelogram ...
Σελίδα 56
... square of BC ; and therefore also the side DC is equal to the side BC . And because the side DA is equal † to AB , and AC common to the two triangles DAC , BAC , the two DA , AC are equal to the two BA , AC , each to each ; and the base ...
... square of BC ; and therefore also the side DC is equal to the side BC . And because the side DA is equal † to AB , and AC common to the two triangles DAC , BAC , the two DA , AC are equal to the two BA , AC , each to each ; and the base ...
Σελίδα 59
... AC , shall be equal to the square of AB . # 46 . 1 . # 31 . 1 . Upon AB describe ADEB , and through C parallel to AD or BE . A C B the square draw * CF , Then AE is equal to the rectangles AF , CE : but AE is the square of AB ; and AF ...
... AC , shall be equal to the square of AB . # 46 . 1 . # 31 . 1 . Upon AB describe ADEB , and through C parallel to AD or BE . A C B the square draw * CF , Then AE is equal to the rectangles AF , CE : but AE is the square of AB ; and AF ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements [Book 1-6] With Corrections, by J.R. Young Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 105 - 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 50 - 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 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 65 - 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.
Σελίδα 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 172 - 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 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Σελίδα 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.