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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Σελίδα 39
... Gnomon . " Thus the parallelogram HG , toge- ther with the complements AF , FC , H is the gnomon , which is more briefly expressed by the letters B F K AGK , or EHC , which are at the opposite angles of the pa- rallelograms which make ...
... Gnomon . " Thus the parallelogram HG , toge- ther with the complements AF , FC , H is the gnomon , which is more briefly expressed by the letters B F K AGK , or EHC , which are at the opposite angles of the pa- rallelograms which make ...
Σελίδα 43
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : To each of these add LG , which is equal ( I. 4. Cor . ) to the square of CD , therefore the gnomon GMG , together with LG , is equal to the rectangle AD , DB ...
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : To each of these add LG , which is equal ( I. 4. Cor . ) to the square of CD , therefore the gnomon GMG , together with LG , is equal to the rectangle AD , DB ...
Σελίδα 44
... gnomon CMG and the figure LG : But the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Where- fore , if a ...
... gnomon CMG and the figure LG : But the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Where- fore , if a ...
Σελίδα 45
... gnomon AOH , are quadruple of AK : And because AK is the rectangle contained by AB , BC , for BK is equal to BC , therefore four times the rectangle AB , BC is qua- druple of AK : But the gnomon AOH was demonstrated to be quadruple of ...
... gnomon AOH , are quadruple of AK : And because AK is the rectangle contained by AB , BC , for BK is equal to BC , therefore four times the rectangle AB , BC is qua- druple of AK : But the gnomon AOH was demonstrated to be quadruple of ...
Σελίδα 46
... gnomon AOH and the square XH : But the gnomon AOH and XH make up the figure AEFD , which is the square of AD : Therefore four times the rectangle AB , BC , together with the square of AC , is equal to the square of AD , that is , of AB ...
... gnomon AOH and the square XH : But the gnomon AOH and XH make up the figure AEFD , which is the square of AD : Therefore four times the rectangle AB , BC , together with the square of AC , is equal to the square of AD , that is , of AB ...
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.