Selected quad for the lemma: hand_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
hand_n	call_v	left_a	right_a	6,194	5	6.0677	4	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A59151	The sea-gunner shewing the practical part of gunnery as it is used at sea : and, as an introduction thereto, there is exhibited two compendiums, one of vulgar, the other of decimal arithmetick, with necessary tables relating to that art : to which is added an appendix, shewing the use of a proportional scale gunnery, and the use off the sea-gunners rule ... / composed by John Seller, Senior.	Seller, John, fl. 1658-1698.	1691 (1691)	Wing S2487; ESTC R16510	62,819	273

given viz. 63 and Subtract the 49 from the First Square and place the Remainder orderly underneath the Line which is 14 to which Remainder being down the next Squares of the Number propounded and place them on the Right hand of the said Remainder and may now be called the Resolvend Then double the Root being the Number placed in the Quotient which is 14 and place them on the Left hand of the Resolvend like a Divisor parted off with a Crooked Line Then demand how often that Divisor is contained in the Resolvend which may be now called the Dividend proceeding in all respects as you do in Division and write the answer in the Quotient on the Right hand of the Divisor then if you ask how often the Divisor 149 is found in the Dividend 1404 the Answer is 9 times Therefore write 9 in the Quotient and also after the Divisor 14. Then Multiply all the Numbers which stand on the Left hand of the Resolvend viz. before the Crooked Line and write the Product orderly underneath the Resolvend then having drawn a Line under the said Product subtract it from the Resolvend and subscribe the Remainder under the Line which is 63 unto which Number bring down the remaining Figures of the Resolvend and then there will be 6336 at the Left hand of which number draw another Crooked Line then double the Quotient which is 158 and set it on the Left hand of the said Crooked Line then demand how often you may have 158 in 633 the Answer is 4 which 4 must be placed in the Quotient then multiply that by each Figure of the Divisor and subscribe the Product orderly under the Dividend and subtract it therefrom and there remains 16 so the work is finished and the Square Root of that Number 630436 is 794 and 16 which remains intimates that the Root is something greater than 794 but less than 795 yet how much greater than 794 is not yet discovered by any Rules of Art But farther Progress may be made for a nearer discovery of the truth but in this case it being but a small difference I shall wave it To Extract the Square Root by the Logarithms The Rule HAlf the Logarithm of any Number is the Logarithm of the Square Root thereof Example Let the Square Number given be 5625 The Logarithm of 625 is 2,79588 The half thereof is 1,39794 which is the Logarithm of 25 the Root of the said Number By Gunter's Scale To Extract the Square Root is to find a mean proportional Number between I and the Number given therefore divide the Space between them into Two Equal parts and that shall be the Root sought Example Let it be required to find the Square Root of 144 Divide the distance betwixt I and 144 equally and the Compasses will fall on 12 the Root sought The EXTRACTION of the CVBE ROOT THe Extraction of the Cube Root is that by which having a Number given another may be found which being first Multiplied by itself and then by the Product produceth the Number given 〈◊〉 the Extraction of the Cube Root the ●●●ber propounded is always conceived to be a Cubical Number that is a certain Number of little Cubes comprehended within one entire great Cube so that the Root of any perfect Cubical Number is a Right Line of a Solid Body containing 6 Equal Sides which constitutes as many Square Superficies or a Number Multiplied twice in itself which in the Solid hath length breadth and depth as may more plainly appear in this Annexed Cubical Figure A Cube Number is either Single or Compound A Single Cube Number is that which is produced by the Multiplication of one single Figure first by itself and then by the Product and is always less than 100 so 64 is a single Cube Number produced by the Multiplication of 4 First by itself and then by the Product as in the Margin A Compound Cube Number is when there are Two Figures in the Root All the Single Cube Numbers and Square Numbers together with their respective Roots are expressed in this Table following Cubes 1 8 27 64 125 216 343 512 729 1000 Squar 1 4 9 16 25 36 49 64 81 100 Roots 1 2 3 4 5 6 7 8 9 10 To prepare a Cube Number for Extraction The Rule PUt a Point over the First place thereof towards the Right hand viz. the place of Unites then passing over the Second and Third places put another over the Fourth and passing over the Fifth and Sixth put another over the Seventh always observing the same order in intermitting Two Places between every Two Adjacent Points place as many Points as the Number will permit as may plainly appear in this Example Let 1728 be the Number given place the Points according to this Rule Which done draw a Crooked Line on the Right hand of the Number to signify a Quotient then find the Cube Root of the First Cube which is 1 as you may see in the Table which 1 set in the Quotient Then subscribe the Cube of the Root placed in the Quotient under the First Cube of the Number given which in this Example is 1. Then draw a Line under the Cube subscribed aforesaid and subtract this Cube from the First Cube and place the Remainder orderly underneath the Line which in this Example is nothing to which Remainder bring down the ne x Cube which is 728 placing it on the Right hand of the Remainder which number so placed may be called the Resolvend having drawn a Line underneath the Resolvend Square the Root in the Quotient that is multiply it in itself and subscribe 3 the Triple of the said Square or Product under the Resolvend and place it under 7 the place of Hundreds Then Triple the Root or Number in the Quotient which is 3 and subscribe this Triple Number in such a manner that the First place thereof the place of Unites may stand under the Second place the place of Tens in the Resolvend which Triple is Three which I place under 2 Then the Triple Square of the Root and the Triple of the Root being so placed draw a Line under them and add them together the Sum is 33 for a Divisor Then let the whole Resolvend except the First place thereof towards the Right hand viz. the place of Unites be esteemed as a Dividend then demanding how often the First Figure towards the Left hand of the Divisor is contained in the correspondent part of the Dividend write the Answer in the Quotient for if I ask how many times Three in 7 the Answer is twice therefore I place 2 in the Quotient Then draw another Line under the work and multiply the Triple Square before subscribed under 7 by the last Figure placed in the Quotient which is 2 and say 2 times 3 is 6 which Product I subscribe under the said Triple Square viz. under the 3 which stands under the 7 as you may see in the work Then Multiply the

therefore I cut off the last Figures in the Quotient which being added to the 3 Figures in the Divisor makes them equal to the Fraction in the Dividend which is 5 Cyphers so the general Rule is made good as you may see in the work Example 2. To divide a Fraction by a whole Number Here according to the 9th Note I prefix a Cypher before the Quotient there being after the Division is finished only Four Figures in the Quotient so then there are 5 Figures in the Dividend and 5 in the Quotient according to the general Rule as you may see in the work Example 3. To Divide a whole Number and a Fraction by a Fraction Here you see 4 Figures are cut off in the Quotient which with the 2 in the Divisor makes 6 which is equal to the Decimal parts in the Dividend according to the General Rule in pag. 37 aforegoing Example 4. To divide a Fraction by a whole Number and a Fraction Here are 7 Decimals in the Dividend and when the Division is finished there are 4 Figures in the Quotient which with the 2 in the Divisor makes but 6 Therefore according to the 9th note I prefix a Cypher before the Quotient on the left hand and then they are equal Example 5. To divide a Fraction by a Fraction According to the General Rule I cut off 4 Figures to the Right hand in the Quotient which makes those in the Divisor equal to those in the Dividend Example 6. To divide a whole Number and a Fraction by a whole Number Here are only 2 Figures to be separated in the Quotient there being no Decimals in the Divisor and only 2 in the Dividend Example 7. To Divide a whole Number by a whole Number and a Fraction There being 7 Decimals in the Dividend I therefore cut off 5 Figures in the Quotient which with the 2 in the Divisor make 7 according to the General Rule p. 37. Example 8. To divide a whole Number and a Fraction by a whole Number and a Fraction According to Note 9th in pag. 34 add Cyphers to the Dividend and when the work is finished I find 5 Figures in the Quotient 3 of which must be cut off that they may make those of the Divisor 6 equal to the Decimals in the Dividend according to the Rule A Decimal Table of Pence and Farthings Pence Farth Decimal 1 0010416 2 0020833 3 0031250 I 0041666 1 0052083 2 0062500 3 0072916 II 0083333 1 0093750 2 0104166 3 0114583 III 0125000 1 0135416 2 0145833 3 0156250 IV 0166666 1 0177083 2 0187500 3 0197916 V 0208333 1 0218750 2 0229166 3 0239583 VI 0250000 1 0260416 2 0270833 3 0281250 VII 0291666 1 0302083 2 0312500 3 0322916 VIII 0333333 1 0343750 2 0354166 3 0364583 IX 0375000 1 0385416 2 0395833 3 0406250 X 0416666 1 0427083 2 0437500 3 0447916 XI 0458333 1 0468750 2 0479166 3 0489583 XII 0500000 1 0510416 2 0520833 3 0531250 XIII 0541666 1 0552083 2 0562500 3 0572916 XIV 0583333 1 0593750 2 0604166 3 0614583 XV 0625000 1 0635416 2 0645833 3 0656250 XVI 0666666 1 0677083 2 0687500 3 0697916 XVII 0708333 1 0718750 2 0729166 3 0739583 XVIII 0750000 1 0760416 2 0770833 3 0781250 XIX 0791666 1 0802083 2 0812500 3 0822916 XX 0833333 1 0843750 2 0854166 3 0864183 XXI 0875000 1 0885416 2 0895833 3 0906250 XXII 0916666 1 0927084 2 0937500 3 0947916 XXIII 0958333 1 0968750 2 0979166 3 0989583 XXIV 1000000 A Table of Decimals of one Pound Sterling in Shillings Sh. Decim 1 050000 2 100000 3 150000 4 200000 5 250000 6 300000 7 350000 8 400000 9 450000 10 500000 11 550000 12 600000 13 650000 14 700000 15 750000 16 800000 17 850000 18 900000 19 950000 20 100000 21 105000 22 110000 23 115000 24 120000 25 125000 26 130000 27 1350000 28 1400000 29 1450000 30 1500000 31 1550000 A Table of the Decimals of a Foot to every Inch and Eighth part of an Inch. Inches 8 Part. Decimal 1 001041 2 002083 3 003125 4 004166 5 005208 6 006250 7 007291 I 008333 1 009375 2 010416 3 011458 4 012500 5 013541 6 014583 7 015625 II 016666 1 017708 2 018750 3 019791 4 020833 5 021875 6 022926 7 023958 III 025000 1 026041 2 027208 3 028125 4 029166 5 030200 6 031299 7 032291 IV 033333 Inches 8 Part. Decimal 1 034385 2 035416 3 037395 4 037499 5 038541 6 039583 7 040625 V 041666 1 042610 2 043750 3 044718 4 045833 5 046875 6 047927 7 048854 VI 050000 1 051104 2 052083 3 053125 4 054166 5 055207 6 056250 7 057291 VII 058333 1 059375 2 051041 3 061457 4 062500 5 063531 6 064583 7 065625 VIII 066000 1 067610 2 068750 3 069896 4 070833 5 071875 6 072916 7 073958 IX 075000 1 076041 2 077083 3 078125 4 079166 5 080208 6 081250 7 082291 X 083333 1 084375 2 085416 3 086457 4 087500 5 088541 6 089687 7 090625 XI 091666 1 092708 2 093750 3 094791 4 095833 5 096875 6 097926 7 098958 XII 100000 The Calculating of this Table is by Dividing every Inch and 8 Parts by 96 because there are so many parts in the Foot every Inch being divided into 8 Parts serving to Reduce Inches and 8 Parts to the Decimals of a Foot or the contrary An Explanation of this Table The First Column shews the Inches and Eight parts of a Foot and the Second Column shews the Decimal Number answering thereto Example Seek for 11 Inches and 8 4 or a half in the First Collumn and in the next you will find the Decimal thereof 095833. CHAP. III. THE EXTRACTION OF THE Square Root THe Extraction of the Square Root is that by which having a number given another number may be found which being Multiplied by itself produceth the number required Any Square number being given to be Extracted thus it may be prepared According to this Rule put a Point over the first place thereof to the Right hand being the place of Unites then proceeding towards the left hand pass over the second place and put a Point over the third place also passing over the Fourth place put another Point over the Fifth and so forward in such manner that between every Two Points which are next one to another so that one place may be intermitted according to this Example 630436. Suppose the Square Root of this Number be required the First Point is to be placed over 6 and the Second over 4 and so of the rest as you see in the Example and note that as many Points as are placed in that manner of so many Figures will the Root be To fit it for operation draw a crooked Line on the Right hand of the Number propounded for Extraction then find the Root of the First Square and place it in the Quotient which in this Example is found to be 7 Then Square the Quotient which is 49 and place it under the first Square of the Number