The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 σελίδες |
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Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 44
... construct the figure as in the preceding propositions : And because AG is equal ( 1. 43. ) to GE , add to each of them CK ; the whole AK is therefore equal to the whole CE ; therefore AK , CE are double of AK ; but AK , CE are the ...
... construct the figure as in the preceding propositions : And because AG is equal ( 1. 43. ) to GE , add to each of them CK ; the whole AK is therefore equal to the whole CE ; therefore AK , CE are double of AK ; but AK , CE are the ...
Σελίδα 45
... construct two figures such as in the preceding . Because CB is equal to BD , and that CB is equal ( 1. 34. ) to GK , and BD to KN ; therefore GK is equal to KN : For the same reason , PR is equal to RO ; and because CB is equal to BD ...
... construct two figures such as in the preceding . Because CB is equal to BD , and that CB is equal ( 1. 34. ) to GK , and BD to KN ; therefore GK is equal to KN : For the same reason , PR is equal to RO ; and because CB is equal to BD ...
Σελίδα 87
... construct the triangle . 13. To construct a right - angled triangle , having given the hypotenuse , and one of the acute angles equal to one third a right angle . Show that the side opposite to the given angle is equal to one half the ...
... construct the triangle . 13. To construct a right - angled triangle , having given the hypotenuse , and one of the acute angles equal to one third a right angle . Show that the side opposite to the given angle is equal to one half the ...
Σελίδα 90
... constructed upon the two diagonals of the rhombus . 29. Parallelograms whose sides and angles are equal are themselves equal . 30. The lines which join the middle points of the three sides of a triangle , divide it into four equal ...
... constructed upon the two diagonals of the rhombus . 29. Parallelograms whose sides and angles are equal are themselves equal . 30. The lines which join the middle points of the three sides of a triangle , divide it into four equal ...
Σελίδα 91
... construct it . E K Let AB be the sum of the three sides , and c and D the two given angles : It is required to describe a triangle , which shall have the sum C of its sides equal to AB , and the angles at the base equal to C and D ...
... construct it . E K Let AB be the sum of the three sides , and c and D the two given angles : It is required to describe a triangle , which shall have the sum C of its sides equal to AB , and the angles at the base equal to C and D ...
Άλλες εκδόσεις - Προβολή όλων
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2014 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle EDF angle equal angles CBA base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AB straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle
Δημοφιλή αποσπάσματα
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 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 20 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Σελίδα 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Σελίδα 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Σελίδα 7 - 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.