Changing the medium upon which God's law is written from stone to our hearts does not change the content of what it instructs us to do, so the command to keep the 7th day holy written on stone instructs us to do the same thing as the command to keep the 7th day holy written on our hearts. In Leviticus 19:17, it instructs not to hate our brother, so that is nothing that is not already in accordance with what God's law instructs.
The Ten Commandments are based on five principles that are expressed differently when in regard to our vertical relationship with our Creator(s) or with our horizontal relationships with our neighbors, such as with the 2nd Commandment against committing idolatry being to our relationship with God what the 7th Commandment against committing adultery is to our relationship with our neighbor. If we correctly understand the five principles that the Ten Commandments are examples of, then we will also understand negative commands to refrain from doing something as being commands to do the reverse, such as with the command against murder also being the command to value life and the command against committing theft also being the command to be generous.
I'm a Lutheran, the 2nd Commandment states not to profane God's name. The command to not worship idols is part of the 1st Commandment, "You shall have no other gods". The 7th Commandment is "Do not steal", the command against adultery is the 6th Commandment.
Here is the Decalogue:
1. "You shall have no other gods before Me"
2. "You shall not take the Name of the LORD your God in vain."
3. "You shall sanctify the Sabbath."
4. "You shall honor your mother and your father."
5. "You shall not kill."
6. "You shall not commit adultery."
7. "You shall not steal."
8. "You shall not bear false witness against your neighbor."
9. "You shall not covet your neighbor's house."
10. "You shall not covet your neighbor's wife, nor man-servant, nor maid-servant, nor his cattle, nor anything that is his."
There are a lot of ways to split the Decalogue up. As a Lutheran I follow the traditional numbering which has been in general use among Christians in the West for most of history. The majority of Protestants, however, follow the numbering system which John Calvin came up with. This is, it would seem, the numbering system you are using.
If you are trying to glean a spiritual significance based on a specific way to enumerate the Decalogue, then I'd recommend not.
Yes, the Decalogue touches upon love of God and love of neighbor. I already said that, that's something Christians have agreed upon for a very long time.
But it's not as though there are 5 that are "vertical" and 5 that are "horizontal".
In the traditional Western system of numbering only 2 of the commandments directly deal with God: You shall have no other gods, and You shall not take the Lord's name in vain.
The command to sanctify the Sabbath is a neighborly commandment (Exodus 20:8-11), it's about providing rest for others, including even our beasts of burden. This sanctity of rest extends even to the land itself. The 3rd Commandment isn't vertical, it's horizontal--our relationship toward other people and God's creation. That's why the Lord Jesus Christ said, "The Sabbath was made for man, not man for the Sabbath". Most of the Decalogue is horizontal. Using the numbering system that most Western Christians have used throughout history, 8 of the 10 commandments are about how we relate to other people.
Tangential addendum: If we count up the "You shall" and You shall nots", along with "Sanctify the Sabbath" and "Honor your mother and father", we actually get
Eleven. If we add "I am the Lord your God who brought you out of Egypt", that's actually Twelve. But Exodus 34:28 specifically mentions the "Ten Words" on the tablets of stone. As such Jewish and Christian tradition(s) have always tried to fit the texts of Exodus 20 and Deuteronomy 5 in such a way that we count 10 Commandments, Ten Words, The Decalogue. The text(s) themselves don't explicitly show a numbering system; and as noted, it isn't as easy as simply counting all the "You shall"/"You shall not"s, doing that gets us more than 10. The traditional Rabbinic way counts "I am the Lord your God that brought you out of Egypt" as the 1st, with the 2nd being "You shall have no other gods before Me" (this includes the prohibition against idols), and so forth. St. Augustine began the count with "You shall have no other gods" which includes the prohibition against making idols, with the 2nd being "You shall not take the name of the Lord your God in vain". I mentioned earlier in this post that John Calvin introduced a new numbering system, his broke up the traditional 1st Commandment into two: 1. "You shall have no other gods before Me" and 2. "You shall not make for yourselves any graven images". The Eastern Orthodox also have a numbering system different from both the Western Augustinian and Calvinist traditions. And let's not even mention the Samaritans, in the Samaritan Pentateuch the content of the mitzvot themselves are different, as the Samaritans include worshipping at Mt. Gerizim to be one of the Ten Commandments; and this is most certainly an obvious anti-Jerusalem bias rooted in the ancient division between Samaritan Israelites and Jewish Israelites.
-CryptoLutheran