The Elements of Euclid, books i. to vi., with deductions, appendices and historical notes, by J.S. Mackay. [With] Key1884 |
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Página 4
... means always , to cut into two equal parts . 10. When a straight line stands on another straight line , and makes the adjacent angles equal to each other , each of the angles is called a right angle ; and the straight line which stands ...
... means always , to cut into two equal parts . 10. When a straight line stands on another straight line , and makes the adjacent angles equal to each other , each of the angles is called a right angle ; and the straight line which stands ...
Página 6
... mean any combination of points , lines , or surfaces . 16. A circle is a plane figure contained by one ( curved ) line which is called the circumference , and is such that all straight lines drawn from a certain point within the figure ...
... mean any combination of points , lines , or surfaces . 16. A circle is a plane figure contained by one ( curved ) line which is called the circumference , and is such that all straight lines drawn from a certain point within the figure ...
Página 11
... means not to make a straight line when there is none , but when there is a straight line already , to make it longer . The third postulate is sometimes expressed , ' a circle may be described with any centre and any radius . ' That ...
... means not to make a straight line when there is none , but when there is a straight line already , to make it longer . The third postulate is sometimes expressed , ' a circle may be described with any centre and any radius . ' That ...
Página 18
... means of other truths already known . The truths already known are either axioms or theorems . A problem is a construction which is to be made by means of certain instruments . The instruments allowed to be used are ( see the remarks on ...
... means of other truths already known . The truths already known are either axioms or theorems . A problem is a construction which is to be made by means of certain instruments . The instruments allowed to be used are ( see the remarks on ...
Página 20
... means the forty - seventh proposition of the first book . In the figures to certain of the theorems , it will be seen that some lines are thick , and some dotted . The thick lines are those which are given , the dotted lines are those ...
... means the forty - seventh proposition of the first book . In the figures to certain of the theorems , it will be seen that some lines are thick , and some dotted . The thick lines are those which are given , the dotted lines are those ...
Otras ediciones - Ver todas
The Elements of Euclid, books i. to vi., with deductions, appendices and ... Euclides Vista completa - 1885 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon Mackay,John Sturgeon Euclides Sin vista previa disponible - 2018 |
The Elements of Euclid, Books I. to VI., with Deductions, Appendices and ... John Sturgeon MacKay,John Sturgeon Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.